Abstract: Space manipulator is one of the key technologies to carry out on-orbit servicing and maintenance missions in the future. Until now, it is still a vast challenging mission to capture a non-cooperative target satellite by using a space robot, especially when the motion of the target satellite is tumbling. How to design a feasible and optimal grasping strategy is very important for the successfully capturing of non-cooperative target. Based on the concept of the Clamped B Spline, this paper investigates an optimal grasp planner for a kinematically redundant space manipulator to capture an arbitrarily rotating target, such as space debris, dysfunctional satellites, etc. The kinematics and dynamics of the space robotic system and non-cooperative target in pre- and post-capture phases are firstly introduced as the foundation for designing the grasp planner. With consideration of the kineto-statics duality of the non-cooperative target captured by a space robot, the concept of the force manipulability ellipsoid was derived and employed as an optimization index in the following grasp planning strategy design. Subsequently, the space robotic optimal grasping time and the target's terminal motion states are determined with consideration of the robotic capability map, the target motion prediction and the grasping direction of the space robotic end-effector. Furthermore, the joint trajectories are parameterized with time normalization using the clamped B-spline curves. The grasp planner of the space robot is then transformed as a multi-constraint, multi-objective nonlinear optimization issue with consideration of the space robotic joint angle, velocity, collision avoidance and end-effector's grasping cone limits, and solved by a constrained particle swarm optimization algorithm with adaptive inertia parameters. The designed grasp planning strategy is applied to a seven degree-of-freedom kinematically redundant manipulator mounted on a free-floating spacecraft base, and the successful capturing of a tumbling target satellite in space is realized. Simulation results are presented and demonstrated the feasibility and effectiveness of the proposed method.