Abstract: The trajectory tracking control of a space robot system with flexible joints in the joint space with uncontrolled base and uncertain parameters is discussed. From the conservations of the linear and angular momentum, the dynamic equations of the system are derived by the Lagrange method. A joint flexible compensation is used to reduce the system's joint flexibility in order to reduce the effect of the flexible joints on the system's control precision. As for the uncertain parameters, the singular perturbation method is used to design an adaptive back-stepping sliding mode control with the disturbance observation to track the desired trajectory in the joint space. With the proposed scheme, it is not required to linearly parameterize the dynamic equation of the system, and the controller is simple and achieves the accurate tracking control of the space robot joint movement. A planar space robot with two links is simulated to verity the feasibility of the proposed control scheme.