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.