In a multichannel geosynchronous spaceborne–airborne bistatic synthetic aperture radar (GEO-SA-BiSAR) system, the airborne receiver can obtain high-resolution microwave images with good signal-to-noise ratios (SNRs) by passively receiving echoes from the desired area. Since the Doppler modulation and range history of a moving target are obviously different from a stationary target, a signal geometry model for moving targets in multichannel GEO-SA-BiSAR is established in this paper. According to simulation results, the along track velocity introduces target defocusing in azimuth, and the slant range velocity mainly causes multiple false targets. To resolve these problems, a modified multichannel reconstruction method in azimuth channel GEO-SA-BiSAR is proposed according to the azimuth multichannel impulse response of the imaged moving target. Before azimuth multichannel raw data combination, both spatial-variant range cell migration correction (RCMC) and azimuth nonlinear chirp scaling (ANLCS) should be performed to reduce the influence of the range offset and lower the Doppler bandwidth of the whole raw data, respectively. Afterward, a novel azimuth multichannel reconstruction algorithm is carried out via the modified reconstruction matrix based on the estimated target velocity. The target slant range velocity estimation is implemented by introducing the signal intensity ratio (SIR). Compared with the conventional method for the stationary target to handle the raw data of the moving target, the false targets could be obviously suppressed by using the proposed approach. Imaging results on both simulated point and distributed scene targets validate the proposed multichannel reconstruction approach.