A global approximation convergence controller is designed for the free-floating space robot system, which solves the robustness problem of the system when there is initial state error or external disturbance.Firstly, the controller is designed based on the state space equation of the system, which isolates the output characteristics from control gains, and exhibits strong robustness against model uncertainties and external disturbance. Meanwhile, the control method completely avoids the high-complexity issue raised by backstepping-like control approaches.Then, it is proved theoretically that the proposed controller can ensure the robot system to track the desired path. Finally, the proposed controller and the robust compensation controller are used respectively for simulation analysis to a single-arm six-DOF space robot system.The simulation results confirm the superiority of the proposed controller.