During the transposition of a target satellite, dynamic coupling between the target satellite, the manipulators, and the base frequently leads to disturbances in the base’s attitude. To deal with the issue, this paper proposed a pose stabilization method for the base of the post-capture combined system using the feedforward compensation PD control. Firstly, the mission sequence for repositioning a target satellite using a discrete-serpentine heterogeneous dual-arm space robot (DSHDASR) was analyzed. The dynamics model of the combined system, composed of the DSHDASR and a target satellite, was established based on the Newton–Euler recursive formulation. Then, the pose stabilization method integrating dynamic feedforward compensation and PD control was developed to stabilize the base of the combined system. Finally, the mission of target satellite transposition was simulated through the co-simulation model. Compared with the traditional control algorithms, the position accuracy and attitude accuracy for the proposed method showed an overall improvement. The results demonstrated that the proposed method significantly reduced base pose errors under high-load and disturbed conditions.