In order to make the space manipulator with joint effectiveness partial loss failure (JEPLF) complete expected task, a singularity avoidance trajectory tracking control method is proposed. Firstly, after modelling the space manipulator with JEPLF, the velocity coupling between joints, base, end-effector is analyzed, and the coupling between the joints’ control torque and the acceleration of base, end-effector is analyzed, the joints are divided into healthy joints and faulty joint. Secondly, taking expected motion of end-effector as target, actual motion as feedback, the control rate is designed so that the end-effector’s position and attitude track the expected value simultaneously. Then, the manipulability optimization model is designed and introduced to the control rate to realize the singularity avoidance trajectory tracking control. Finally, it is proved that the trajectory tracking control method is correct and effective. The simulation shows that when general JEPLF occurs, the end-effector’s position and attitude errors approach to zero quickly, the end-effector tracks desired trajectory smoothly, the singular configuration is avoided, and the manipulability is improved at every moment by using the proposed method.