Abstract: In order to perform an OOS (on-orbit servicing) mission of capturing a space non-cooperative target by space robot, this paper proposes a hierarchical coordinated path planning method for the free-floating dual-arm space robot, in which we consider the robot's constraints both kinematic and dynamic at the same time. First of all, a feasible end-effectors' path is initially planned via a state-of-the-art sampling-based method, named RRT* algorithm, in the Cartesian space, in which the sampling space is separated for two arms for the sake of possible self-collision avoidances of the dual-arm system during the high level of the path planning stage. Secondly, quartic splines are employed to smooth the path planned by RRT* algorithm during the low level of the trajectory planning stage. By designing the first-order derivative, the second-order derivative as well as the third-order derivative of these quartic splines, continuous differential constraints of the robot's path are well guaranteed. More importantly, we should integrate the robot's dynamic constraints within the design of differential constraints, such as the initial velocity, the initial acceleration and the final velocity of the end-effectors. After that, a smooth trajectory considering certain boundary constraints is obtained, which is dynamically feasible for the robot execution. Finally, the time of the whole path execution is calculated by considering the maximum physical limitation of the end-effectors. The minimum upper limit of maximum velocity and maximum acceleration of planned path of the end-effectors over its physical limitation is the minimum execution time. The proposed path planning method could design a coordinated path satisfying certain waypoints constraints for the robot. Besides, the physical limitation of the robot is also considered for the planned path. Moreover, the proposed path planning method is successfully validated on a free-floating dual-arm space robot and simulation results demonstrate the effectiveness of the proposed path planning method.