Flexible appendages, such as solar panels, communication antennas and other large structures, are mounted on the base of a space robot and target satellite. The vibration of the flexible structure is excited by operations of a space manipulator. It is very challenging to control the vibration of large flexible appendages for on-orbit operation and, especially when the manipulator operates a non-cooperative target with unknown structural parameters and vibration information. In this study, a hybrid control method is proposed based on wave-based control and PD control methods to control the motion of a manipulator while suppressing the vibration of appendages. First, the rigid-flexible coupled dynamic model of a compounded system is established.This is followed by designing a hybrid control strategy combining wave-based control and PD control for restto-rest maneuvers based on the characteristics of the compounded system. Finally, the simulation of a 3D compounded system is provided to verify the effectiveness of the presented approach. The simulation results indicate that the space robot can successfully berth the target while suppressing the vibrations of the structure. The vibration of the flexible structure is excited by operations of a space manipulator. It is very challenging to control the vibration of large flexible appendages for on-orbit operation and, especially when the manipulator operates a non-cooperative target with unknown structural parameters and vibration information. In this study, a hybrid control method proposed is based on wave-based control and PD control methods to control the motion of a manipulator while suppressing the vibration of appendages. First, the rigid-flexible coupled dynamic model of a compounded system is established. This is followed by designing a hybrid control strategy and wave-based control and PD control for restto- rest maneuvers based on the characteristics of the compounded system. Finally, the simulation of a 3D compounded system is provided to v erify the effectiveness of the presented approach. The simulation results indicate that the space robot can successfully berth the target while suppressing the vibrations of the structure.