As the technology of space science develops rapidly, space robot system is expected to capture the noncooperative satellite on-orbit. Space robot with dual-arm obviously has more comparative advantage in this respect compared with the one with single arm. Because of the complicated condition in outer space it makes the dynamics and control problems related to satellite-capturing operation by space robot system with dual-arm to be extremely complicated, and there are some unique characteristics, such as, nonholonomic dynamics restriction, change of system configuration, transfer of linear momentum, angular momentum and energy, topology transfer from open to closed loop system, and the constraints of closed-loop geometry and kinematics during satellite-capturing operation. In this paper, the dynamic evolution for space robot with dual-arm capturing a spin satellite and calm control for unstable closed chain composite system are discussed. At first, with the Lagrangian approach, the dynamic model of open chain space robot with dual-arm before capture operation is established, and dynamic model of satellite is derived by Newton-Euler method. On that basis, based on the law of conservation of momentum and the law of force transfer, the impact effect after collision of space robot with dual-arm to capture the target is analyzed and solved by the process of integration and simplification, and the suitable capture operation strategy is given. Closed chain constraint equations are obtained by the constraints of closed-loop geometry and kinematics of closed chain system. With the closed chain constraint equations, the composite system dynamic model is derived. For the unstable closed chain composite system after the capture, the fuzzy H∞ control scheme for calm motion is designed. The fuzzy logic system is applied to overcome the influence of uncertainty part and the robust H∞ control item is used to eliminate the approximate error, to guarantee the tracking precision. The global stability of the system is proved by the Lyapunov theory. The weighted minimum-norm theory is introduced to distribute torques guaranteeing that the cooperative operation between manipulators. At last, numerical examples simulated the response of collision are used to verify the efficiency of the control scheme.