The　impact　effect　of　a　free　floating　space　manipulator　during　capturing　a　free　flying　satellite,　and　the　stabilizing　control　after　impact　are　studied.　Firstly,　a　dynamic　model　of　the　space　manipulator　system　is　derived　based　on　kinematic　equation.　And　then,　the　impact　effect　is　evaluated　for　the　space　manipulator　system　during　capturing　a　satellite　based　on　the　momentum　conservation　theory　by　considering　the　kinematic　and　force　transfer　relationships　between　the　manipulator　and　the　satellite　contact　point.　Finally,　for　the　unstable　space　manipulator　system　after　impact,　an　RBF　(radial　basis　function)　neural　network　control　algorithm　is　designed　for　stabilizing　the　motion　of　system.　There　is　no　need　for　the　position　control　of　the　base,　and　the　influence　of　uncertain　satellite　parameters　can　be　compensated.　The　simulation　shows　the　impact　effect　in　the　capturing　process　and　the　validity　of　the　proposed　stabilizing　control　algorithm.