Pulse time-of-arrival (TOA) estimation is the key procedure to construct the measurement in X-ray pulsar navigation.Traditional TOA estimation methods are designed assuming spacecraft to be at rest.However,spacecraft orbit motion introduces doppler effect and causes observed pulse period shift,which makes TOA estimation harder.This paper provides a method based on average cross correlation to solve the problem in orbit motion situation.Instead of direct dopplerfrequency estimation,this idea transplants the static cross correlation method based on epoch folding into dynamic situation by folding at the middle of the observation period to counteract the doppler effect.At certain Doppler frequencies,the average cross correlation method is tested via Monte-Carlo simulation.Results show that the proposed method can output high-precision TOA estimation at small accumulated doppler phases.