To eliminate the impact of the Doppler effects caused by the motion of the Mars explorer, a novel X-ray pulsar navigation method based on a closed-loop filter is proposed. In the pulsar signal observation period, the Doppler velocity predicted by the orbit dynamic model and the prior information is utilised to compensate the X-ray photon time-of-arrival (TOA). However, because of the error in prior information, there is a bias caused by the Doppler compensation in the pulse time-of-arrival. The pulse TOA bias and the Mars explorer's state estimation error are correlated, which results in the decline of the Kalman filter performance. To deal with this problem, we build the TOA measurement model with respect to the state estimation error, and utilise the closed-loop extended Kalman filter (EKF) as the navigation filter, where the predicted state error is adopted as the state estimation. The simulation results demonstrate the feasibility, real-timeliness and effectiveness of the proposed navigation method. The navigation method based on the closed-loop EKF using the measurement model with the Doppler effects is more accurate than the traditional one.