The　dynamics　response　and　control　of　a　free-floating　flexible　space　manipulator　impacted　by　capturing　load　were　analyzed.　The　elastic　deformation　of　flexible　link　of　the　space　manipulator　was　approximately　described　by　using　the　method　of　assumed　modes,　and　the　dynamics　model　of　the　free-floating　space　manipulator　system　was　derived　with　second　Lagrange　equation.　Based　on　the　momentum　conservation　theorem,　the　dynamics　response　evaluation　of　the　free-floating　flexible　space　manipulator　impacted　by　capturing　load　was　presented　by　virtue　of　the　momentum　impulse　method.　Then,　an　adaptive　control　algorithm　was　designed　for　the　stabilization　control　of　the　unstable　free-floating　space　manipulator　after　impacted　by　capturing　load,　and　a　linear　quadratic　optimal　control　algorithm　was　designed　for　suppressing　the　elastic　vibration　of　flexible　link.　The　simulation　results　verify　the　validity　of　the　above　control　algorithms.