An improved dual-microphone adaptive Active Noise Cancellation (ANC) method called IM-RM-LMS is proposed to solve the problem of the bearing sound signal being interfered with by wheel-track contact noise in the TADS. Two microphones, the main microphone and the reference microphone, are used to collect the bearing acoustic signal and the wheel-track contact noise signal, respectively. Due to the different relative spatial positions of the two microphones and the noise source, the noise signal components collected by the two microphones obey different Doppler distortion laws, which makes the LMS-based ANC method ineffective. Therefore, the main research content of this paper is the ANC of two moving sound source signals that obey different Doppler distortion laws. An Inverse Modulation and Re-Modulation (IM-RM) processing is innovatively performed to assimilate the Doppler distortion law of the noise signal components collected by the two microphones. The effectiveness of IM-RM-LMS is verified by simulation and experiment. Compared with the traditional LMS algorithm without considering Doppler assimilation, it can achieve a significantly better denoising effect. This method provides a new theoretical basis for noise cancellation of two moving sound sources obeying different Doppler distortion laws and it is expected to be applied to the noise cancellation of TADS.