The impact dynamics, impact effect, and post-impact unstable motion suppression of free-floating space manipulator capturing a satellite on orbit are analyzed. Firstly, the dynamics equation of free-floating space manipulator is derived using the second Lagrangian equation. Combining the momentum conservation principle, the impact dynamics and effect between the space manipulator end-effector and satellite of the capture process are analyzed with the momentum impulse method. Focusing on the unstable motion of space manipulator due to the above impact effect, a robust adaptive compound control algorithm is designed to suppress the above unstable motion. There is no need to control the free-floating base position to save the jet fuel. Finally, the simulation is proposed to show the impact effect and verify the validity of the control algorithm.