The collision avoidance and compliant control for free-floating space robots on-orbit capture non-cooperative spacecraft is studied. For the reason, a spring class compliant mechanism, rotary series elastic actuator (RSEA), is mounted between the joint motor and the manipulator, its functions are: 1) The deformation of its internal spring can absorb the impact energy of the captured spacecraft on the joints of the space robot; 2) The joint impact torque can be limited to a safe range by combining with the collision avoidance compliant control scheme. First of all, the dynamic models of the space robot and the target spacecraft before capture are obtained by using the Lagrange approach and Newton-Euler method. Then based on the law of conservation of momentum, the constraints of kinematics and the law of force transfer, the integrated dynamic model of the combined system is derived; Finally, considering the post-capture unstable combined system, a collision avoidance and compliant composite error active disturbance rejection control is proposed for the stabilization control. Numerical simulation verifies the effectiveness of the proposed collision avoidance and compliant control method.