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.