diff --git a/sweep/fee_function.go b/sweep/fee_function.go
new file mode 100644
index 000000000..db3fb7851
--- /dev/null
+++ b/sweep/fee_function.go
@@ -0,0 +1,265 @@
+package sweep
+
+import (
+	"errors"
+	"fmt"
+
+	"github.com/btcsuite/btcd/btcutil"
+	"github.com/lightningnetwork/lnd/lnwallet/chainfee"
+)
+
+var (
+	// ErrMaxPosition is returned when trying to increase the position of
+	// the fee function while it's already at its max.
+	ErrMaxPosition = errors.New("position already at max")
+)
+
+// FeeFunction defines an interface that is used to calculate fee rates for
+// transactions. It's expected the implementations use three params, the
+// starting fee rate, the ending fee rate, and number of blocks till deadline
+// block height, to build an algorithm to calculate the fee rate based on the
+// current block height.
+type FeeFunction interface {
+	// FeeRate returns the current fee rate calculated by the fee function.
+	FeeRate() chainfee.SatPerKWeight
+
+	// Increment increases the fee rate by one step. The definition of one
+	// step is up to the implementation. After calling this method, it's
+	// expected to change the state of the fee function such that calling
+	// `FeeRate` again will return the increased value.
+	//
+	// It returns a boolean to indicate whether the fee rate is increased,
+	// as fee bump should not be attempted if the increased fee rate is not
+	// greater than the current fee rate, which may happen if the algorithm
+	// gives the same fee rates at two positions.
+	//
+	// An error is returned when the max fee rate is reached.
+	//
+	// NOTE: we intentionally don't return the new fee rate here, so both
+	// the implementation and the caller are aware of the state change.
+	Increment() (bool, error)
+
+	// IncreaseFeeRate increases the fee rate to the new position
+	// calculated using (width - confTarget). It returns a boolean to
+	// indicate whether the fee rate is increased, and an error if the
+	// position is greater than the width.
+	//
+	// NOTE: this method is provided to allow the caller to increase the
+	// fee rate based on a conf target without taking care of the fee
+	// function's current state (position).
+	IncreaseFeeRate(confTarget uint32) (bool, error)
+}
+
+// LinearFeeFunction implements the FeeFunction interface with a linear
+// function:
+//
+//	feeRate = startingFeeRate + position * delta.
+//	     - width: deadlineBlockHeight - startingBlockHeight
+//	     - delta: (endingFeeRate - startingFeeRate) / width
+//	     - position: currentBlockHeight - startingBlockHeight
+//
+// The fee rate will be capped at endingFeeRate.
+//
+// TODO(yy): implement more functions specified here:
+// - https://github.com/lightningnetwork/lnd/issues/4215
+type LinearFeeFunction struct {
+	// startingFeeRate specifies the initial fee rate to begin with.
+	startingFeeRate chainfee.SatPerKWeight
+
+	// endingFeeRate specifies the max allowed fee rate.
+	endingFeeRate chainfee.SatPerKWeight
+
+	// currentFeeRate specifies the current calculated fee rate.
+	currentFeeRate chainfee.SatPerKWeight
+
+	// width is the number of blocks between the starting block height
+	// and the deadline block height.
+	width uint32
+
+	// position is the number of blocks between the starting block height
+	// and the current block height.
+	position uint32
+
+	// deltaFeeRate is the fee rate increase per block.
+	deltaFeeRate chainfee.SatPerKWeight
+
+	// estimator is the fee estimator used to estimate the fee rate. We use
+	// it to get the initial fee rate and, use it as a benchmark to decide
+	// whether we want to used the estimated fee rate or the calculated fee
+	// rate based on different strategies.
+	estimator chainfee.Estimator
+}
+
+// Compile-time check to ensure LinearFeeFunction satisfies the FeeFunction.
+var _ FeeFunction = (*LinearFeeFunction)(nil)
+
+// NewLinearFeeFunction creates a new linear fee function and initializes it
+// with a starting fee rate which is an estimated value returned from the fee
+// estimator using the initial conf target.
+func NewLinearFeeFunction(maxFeeRate chainfee.SatPerKWeight, confTarget uint32,
+	estimator chainfee.Estimator) (*LinearFeeFunction, error) {
+
+	// Sanity check conf target.
+	if confTarget == 0 {
+		return nil, fmt.Errorf("width must be greater than zero")
+	}
+
+	l := &LinearFeeFunction{
+		endingFeeRate: maxFeeRate,
+		width:         confTarget,
+		estimator:     estimator,
+	}
+
+	// Estimate the initial fee rate.
+	//
+	// NOTE: estimateFeeRate guarantees the returned fee rate is capped by
+	// the ending fee rate, so we don't need to worry about overpay.
+	start, err := l.estimateFeeRate(confTarget)
+	if err != nil {
+		return nil, fmt.Errorf("estimate initial fee rate: %w", err)
+	}
+
+	// Calculate how much fee rate should be increased per block.
+	end := l.endingFeeRate
+	delta := btcutil.Amount(end - start).MulF64(1 / float64(confTarget))
+
+	// We only allow the delta to be zero if the width is one - when the
+	// delta is zero, it means the starting and ending fee rates are the
+	// same, which means there's nothing to increase, so any width greater
+	// than 1 doesn't provide any utility. This could happen when the
+	// sweeper is offered to sweep an input that has passed its deadline.
+	if delta == 0 && l.width != 1 {
+		return nil, fmt.Errorf("fee rate delta is zero")
+	}
+
+	// Attach the calculated values to the fee function.
+	l.startingFeeRate = start
+	l.currentFeeRate = start
+	l.deltaFeeRate = chainfee.SatPerKWeight(delta)
+
+	log.Debugf("Linear fee function initialized with startingFeeRate=%v, "+
+		"endingFeeRate=%v, width=%v, delta=%v", start, end,
+		confTarget, l.deltaFeeRate)
+
+	return l, nil
+}
+
+// FeeRate returns the current fee rate.
+//
+// NOTE: part of the FeeFunction interface.
+func (l *LinearFeeFunction) FeeRate() chainfee.SatPerKWeight {
+	return l.currentFeeRate
+}
+
+// Increment increases the fee rate by one position, returns a boolean to
+// indicate whether the fee rate was increased, and an error if the position is
+// greater than the width. The increased fee rate will be set as the current
+// fee rate, and the internal position will be incremented.
+//
+// NOTE: this method will change the state of the fee function as it increases
+// its current fee rate.
+//
+// NOTE: part of the FeeFunction interface.
+func (l *LinearFeeFunction) Increment() (bool, error) {
+	return l.increaseFeeRate(l.position + 1)
+}
+
+// IncreaseFeeRate calculate a new position using the given conf target, and
+// increases the fee rate to the new position by calling the Increment method.
+//
+// NOTE: this method will change the state of the fee function as it increases
+// its current fee rate.
+//
+// NOTE: part of the FeeFunction interface.
+func (l *LinearFeeFunction) IncreaseFeeRate(confTarget uint32) (bool, error) {
+	// If the new position is already at the end, we return an error.
+	if confTarget == 0 {
+		return false, ErrMaxPosition
+	}
+
+	newPosition := uint32(0)
+
+	// Only calculate the new position when the conf target is less than
+	// the function's width - the width is the initial conf target, and we
+	// expect the current conf target to decrease over time. However, we
+	// still allow the supplied conf target to be greater than the width,
+	// and we won't increase the fee rate in that case.
+	if confTarget < l.width {
+		newPosition = l.width - confTarget
+		log.Tracef("Increasing position from %v to %v", l.position,
+			newPosition)
+	}
+
+	if newPosition <= l.position {
+		log.Tracef("Skipped increase feerate: position=%v, "+
+			"newPosition=%v ", l.position, newPosition)
+
+		return false, nil
+	}
+
+	return l.increaseFeeRate(newPosition)
+}
+
+// increaseFeeRate increases the fee rate by the specified position, returns a
+// boolean to indicate whether the fee rate was increased, and an error if the
+// position is greater than the width. The increased fee rate will be set as
+// the current fee rate, and the internal position will be set to the specified
+// position.
+//
+// NOTE: this method will change the state of the fee function as it increases
+// its current fee rate.
+func (l *LinearFeeFunction) increaseFeeRate(position uint32) (bool, error) {
+	// If the new position is already at the end, we return an error.
+	if l.position >= l.width {
+		return false, ErrMaxPosition
+	}
+
+	// Get the old fee rate.
+	oldFeeRate := l.currentFeeRate
+
+	// Update its internal state.
+	l.position = position
+	l.currentFeeRate = l.feeRateAtPosition(position)
+
+	log.Tracef("Fee rate increased from %v to %v at position %v",
+		oldFeeRate, l.currentFeeRate, l.position)
+
+	return l.currentFeeRate > oldFeeRate, nil
+}
+
+// feeRateAtPosition calculates the fee rate at a given position and caps it at
+// the ending fee rate.
+func (l *LinearFeeFunction) feeRateAtPosition(p uint32) chainfee.SatPerKWeight {
+	if p >= l.width {
+		return l.endingFeeRate
+	}
+
+	feeRateDelta := btcutil.Amount(l.deltaFeeRate).MulF64(float64(p))
+
+	feeRate := l.startingFeeRate + chainfee.SatPerKWeight(feeRateDelta)
+	if feeRate > l.endingFeeRate {
+		return l.endingFeeRate
+	}
+
+	return feeRate
+}
+
+// estimateFeeRate asks the fee estimator to estimate the fee rate based on its
+// conf target.
+func (l *LinearFeeFunction) estimateFeeRate(
+	confTarget uint32) (chainfee.SatPerKWeight, error) {
+
+	fee := FeeEstimateInfo{
+		ConfTarget: confTarget,
+	}
+
+	// endingFeeRate comes from budget/txWeight, which means the returned
+	// fee rate will always be capped by this value, hence we don't need to
+	// worry about overpay.
+	estimatedFeeRate, err := fee.Estimate(l.estimator, l.endingFeeRate)
+	if err != nil {
+		return 0, err
+	}
+
+	return estimatedFeeRate, nil
+}
diff --git a/sweep/fee_function_test.go b/sweep/fee_function_test.go
new file mode 100644
index 000000000..e7f80819a
--- /dev/null
+++ b/sweep/fee_function_test.go
@@ -0,0 +1,247 @@
+package sweep
+
+import (
+	"testing"
+
+	"github.com/lightningnetwork/lnd/lnwallet/chainfee"
+	"github.com/stretchr/testify/require"
+)
+
+// TestLinearFeeFunctionNew tests the NewLinearFeeFunction function.
+func TestLinearFeeFunctionNew(t *testing.T) {
+	t.Parallel()
+
+	rt := require.New(t)
+
+	// Create a mock fee estimator.
+	estimator := &chainfee.MockEstimator{}
+
+	// Create testing params.
+	maxFeeRate := chainfee.SatPerKWeight(10000)
+	estimatedFeeRate := chainfee.SatPerKWeight(500)
+	confTarget := uint32(6)
+
+	// Assert init fee function with zero conf value returns an error.
+	f, err := NewLinearFeeFunction(maxFeeRate, 0, estimator)
+	rt.ErrorContains(err, "width must be greater than zero")
+	rt.Nil(f)
+
+	// When the fee estimator returns an error, it's returned.
+	//
+	// Mock the fee estimator to return an error.
+	estimator.On("EstimateFeePerKW", confTarget).Return(
+		chainfee.SatPerKWeight(0), errDummy).Once()
+
+	f, err = NewLinearFeeFunction(maxFeeRate, confTarget, estimator)
+	rt.ErrorIs(err, errDummy)
+	rt.Nil(f)
+
+	// When the starting feerate is greater than the ending feerate, the
+	// starting feerate is capped.
+	//
+	// Mock the fee estimator to return the fee rate.
+	smallConf := uint32(1)
+	estimator.On("EstimateFeePerKW", smallConf).Return(
+		// The fee rate is greater than the max fee rate.
+		maxFeeRate+1, nil).Once()
+	estimator.On("RelayFeePerKW").Return(estimatedFeeRate).Once()
+
+	f, err = NewLinearFeeFunction(maxFeeRate, smallConf, estimator)
+	rt.NoError(err)
+	rt.NotNil(f)
+
+	// When the calculated fee rate delta is 0, an error should be returned.
+	//
+	// Mock the fee estimator to return the fee rate.
+	estimator.On("EstimateFeePerKW", confTarget).Return(
+		// The starting fee rate is 1 sat/kw less than the max fee rate.
+		maxFeeRate-1, nil).Once()
+	estimator.On("RelayFeePerKW").Return(estimatedFeeRate).Once()
+
+	f, err = NewLinearFeeFunction(maxFeeRate, confTarget, estimator)
+	rt.ErrorContains(err, "fee rate delta is zero")
+	rt.Nil(f)
+
+	// Check a successfully created fee function.
+	//
+	// Mock the fee estimator to return the fee rate.
+	estimator.On("EstimateFeePerKW", confTarget).Return(
+		estimatedFeeRate, nil).Once()
+	estimator.On("RelayFeePerKW").Return(estimatedFeeRate).Once()
+
+	f, err = NewLinearFeeFunction(maxFeeRate, confTarget, estimator)
+	rt.NoError(err)
+	rt.NotNil(f)
+
+	// Assert the internal state.
+	rt.Equal(estimatedFeeRate, f.startingFeeRate)
+	rt.Equal(maxFeeRate, f.endingFeeRate)
+	rt.Equal(estimatedFeeRate, f.currentFeeRate)
+	rt.NotZero(f.deltaFeeRate)
+	rt.Equal(confTarget, f.width)
+}
+
+// TestLinearFeeFunctionFeeRateAtPosition checks the expected feerate is
+// calculated and returned.
+func TestLinearFeeFunctionFeeRateAtPosition(t *testing.T) {
+	t.Parallel()
+
+	rt := require.New(t)
+
+	// Create a fee func which has three positions:
+	// - position 0: 1000
+	// - position 1: 2000
+	// - position 2: 3000
+	f := &LinearFeeFunction{
+		startingFeeRate: 1000,
+		endingFeeRate:   3000,
+		position:        0,
+		deltaFeeRate:    1000,
+		width:           3,
+	}
+
+	testCases := []struct {
+		name            string
+		pos             uint32
+		expectedFeerate chainfee.SatPerKWeight
+	}{
+		{
+			name:            "position 0",
+			pos:             0,
+			expectedFeerate: 1000,
+		},
+		{
+			name:            "position 1",
+			pos:             1,
+			expectedFeerate: 2000,
+		},
+		{
+			name:            "position 2",
+			pos:             2,
+			expectedFeerate: 3000,
+		},
+		{
+			name:            "position 3",
+			pos:             3,
+			expectedFeerate: 3000,
+		},
+	}
+
+	for _, tc := range testCases {
+		tc := tc
+
+		t.Run(tc.name, func(t *testing.T) {
+			t.Parallel()
+
+			result := f.feeRateAtPosition(tc.pos)
+			rt.Equal(tc.expectedFeerate, result)
+		})
+	}
+}
+
+// TestLinearFeeFunctionIncrement checks the internal state is updated
+// correctly when the fee rate is incremented.
+func TestLinearFeeFunctionIncrement(t *testing.T) {
+	t.Parallel()
+
+	rt := require.New(t)
+
+	// Create a mock fee estimator.
+	estimator := &chainfee.MockEstimator{}
+
+	// Create testing params. These params are chosen so the delta value is
+	// 100.
+	maxFeeRate := chainfee.SatPerKWeight(1000)
+	estimatedFeeRate := chainfee.SatPerKWeight(100)
+	confTarget := uint32(9)
+
+	// Mock the fee estimator to return the fee rate.
+	estimator.On("EstimateFeePerKW", confTarget).Return(
+		estimatedFeeRate, nil).Once()
+	estimator.On("RelayFeePerKW").Return(estimatedFeeRate).Once()
+
+	f, err := NewLinearFeeFunction(maxFeeRate, confTarget, estimator)
+	rt.NoError(err)
+
+	// We now increase the position from 1 to 9.
+	for i := uint32(1); i <= confTarget; i++ {
+		// Increase the fee rate.
+		increased, err := f.Increment()
+		rt.NoError(err)
+		rt.True(increased)
+
+		// Assert the internal state.
+		rt.Equal(i, f.position)
+
+		delta := chainfee.SatPerKWeight(i * 100)
+		rt.Equal(estimatedFeeRate+delta, f.currentFeeRate)
+
+		// Check public method returns the expected fee rate.
+		rt.Equal(estimatedFeeRate+delta, f.FeeRate())
+	}
+
+	// Now the position is at 9th, increase it again should give us an
+	// error.
+	increased, err := f.Increment()
+	rt.ErrorIs(err, ErrMaxPosition)
+	rt.False(increased)
+}
+
+// TestLinearFeeFunctionIncreaseFeeRate checks the internal state is updated
+// correctly when the fee rate is increased using conf targets.
+func TestLinearFeeFunctionIncreaseFeeRate(t *testing.T) {
+	t.Parallel()
+
+	rt := require.New(t)
+
+	// Create a mock fee estimator.
+	estimator := &chainfee.MockEstimator{}
+
+	// Create testing params. These params are chosen so the delta value is
+	// 100.
+	maxFeeRate := chainfee.SatPerKWeight(1000)
+	estimatedFeeRate := chainfee.SatPerKWeight(100)
+	confTarget := uint32(9)
+
+	// Mock the fee estimator to return the fee rate.
+	estimator.On("EstimateFeePerKW", confTarget).Return(
+		estimatedFeeRate, nil).Once()
+	estimator.On("RelayFeePerKW").Return(estimatedFeeRate).Once()
+
+	f, err := NewLinearFeeFunction(maxFeeRate, confTarget, estimator)
+	rt.NoError(err)
+
+	// If we are increasing the fee rate using the initial conf target, we
+	// should get a nil error and false.
+	increased, err := f.IncreaseFeeRate(confTarget)
+	rt.NoError(err)
+	rt.False(increased)
+
+	// Test that we are allowed to use a larger conf target.
+	increased, err = f.IncreaseFeeRate(confTarget + 1)
+	rt.NoError(err)
+	rt.False(increased)
+
+	// Test that when we use a conf target of 0, we get an error.
+	increased, err = f.IncreaseFeeRate(0)
+	rt.ErrorIs(err, ErrMaxPosition)
+	rt.False(increased)
+
+	// We now increase the fee rate from conf target 8 to 1 and assert we
+	// get no error and true.
+	for i := uint32(1); i < confTarget; i++ {
+		// Increase the fee rate.
+		increased, err := f.IncreaseFeeRate(confTarget - i)
+		rt.NoError(err)
+		rt.True(increased)
+
+		// Assert the internal state.
+		rt.Equal(i, f.position)
+
+		delta := chainfee.SatPerKWeight(i * 100)
+		rt.Equal(estimatedFeeRate+delta, f.currentFeeRate)
+
+		// Check public method returns the expected fee rate.
+		rt.Equal(estimatedFeeRate+delta, f.FeeRate())
+	}
+}