A space manipulator plays an important role in spacecraft capturing, repairing, maintenance, and so on. However, the harsh space environment will cause its joints fail to work. For a non-redundant manipulator, single joint locked failure will cause it lose one degree of freedom, hence reducing its movement ability. In this paper, the key problems related with the fault-tolerant, including kinematics, workspace and trajectory planning, of a non-redundant space manipulator under single joint failure are handled. Firstly, the analytical inverse kinematics equations are derived for the 5-DOF (degree of freedom) manipulator formed by locking the failure joint of the original 6-DOF manipulator. Then, we define the missions can be completed by the 5-DOF manipulator. According to the constraints of the on-orbital mission, a fault tolerance parameter is defined and a planning method is proposed to generate the reasonable trajectory, based on which, the 5-DOF manipulator can complete the desired tasks. Finally, typical cases are simulated and the simulation results verify the proposed method.