To insure the safety of autonomous approaching and capturing of a non-cooperative tumbling target in the on-orbit operating missions, 6 DOF dynamics model of relative translation and rotation is established to describe the relative motion of two spacecrafts in close distance, and the perturbation induced coupling and dynamic coupling existing in the model are presented to make clear what the coupling effect is. Due to the effects of time-varying and nonlinear terms in the model, the systemized integrator backstepping controller is derived after multi-step recursion with regard to the nonlinear high-order terms. The stability of the controller is proved to be global asymptotic stable based on the Lyapunov’s stability theory. With the consideration of rotating characteristic of the target satellite, a linear synchronization rotating approach strategy along the maximum inertial axes is presented to ensure the safety during the final approach. The validity of approach strategy and the effectiveness of controller is verified by the numerical simulation.