Abstract: This paper studies the computation algorithm of joint driven torque and the control algorithm to capture target for Free Flying Space Robots(FFSR).First, the efficient recursive algorithm of joint driven torque for FFSR is developed. Then, the torque control algorithm combined with Resolved Motion Rate Control(RMRC) based on Generalized Jacobian Matrix (GJM) for capturing target is proposed. Finally, the computer simulation verifies the effectiveness of the proposed method and algorithm.