The　impact　effect　and　post-impact　unstable　motion　stabilization　control　of　flexible　space　manipulator　capturing　the　satellite　were　analyzed.　Firstly,　the　dynamic　model　of　space　manipulator　system　was　derived　by　the　second　Lagrange　equation.　Based　on　the　momentum　conservation　principle　during　the　impact　between　the　space　manipulator　and　satellite,　the　impact　effect　which　would　cause　the　unstable　motion　and　flexible　link　vibration　of　space　manipulator　was　calculated.　Considering　the　above　impact　effect,　a　neural　network　control　algorithm　was　proposed　to　stabilize　the　unstable　motion　and　suppress　the　flexible　vibration.　Finally,　the　numerical　simulation　results　verified　the　validity　of　the　proposed　control　algorithm.　©,　2015,　Huazhong　University　of　Science　and　Technology.　All　right　reserved.