Abstract: The design problem of a joint motion controller for a flexible-joint space robot with an uncontrolled base is discussed. With the linear and angular momentum conservation of the system and a Lagrangian method, the dynamic model of a space robot is established. To realize the control target of joint motion, an adaptive backstepping control scheme for a flexible-joint space robot is proposed via the function approximation technique of neural network. The presented control scheme need not know the information of system parameters, and avoids the measurements and feedback of the position-related variables of the base. Thusly, it is more suitable for practical applications. Numerical simulation results show that the control scheme proposed can obtain the smaller vibration of flexible joints and effectively control the space robot system to accomplish the desired joint motion.