In order to solve the problem of the trajectory tracking control for space robot manipulators with joint actuator faults, an adaptive fault-tolerant control scheme based on a neural network online estimator (NNOE) is proposed. First, a unified expression is designed to describe the types of actuator faults, and the integrated dynamic model is subsequently developed under the Euler-Lagangian framework. Then, the backstepping control approach is utilized to separate actuator faults from the system to accurately characterize their adverse effects on the system. Furthermore, combining the nonlinear mapping architecture of the neural networks and the adaptive adjustment law based on the projection operator, a NNOE is designed to ensure the fault tolerance of the system. Finally, stability analysis is given for the whole system and the effectiveness of the proposed approach is verified.