Abstract: The joint motion control and vibration suppression problems of rigid-flexible space robot with an attitude controlled base were discussed. With Lagrangian method and singular perturbation theory, the singular perturbation model of the system was derived. To guarantee the accurate coordinated motion control of the base attitude and the arm's joints under the effects of unknown system parameters, the compensation control strategy based on Radial Basis Function (RBF) neural network was proposed for the slow subsystem. Simultaneously, the linear quadratic optimal controller was given for the fast subsystem to suppress the elastic vibration of the system. Simulation results demonstrate that the presented control scheme can effectively compensate for the influence of unknown system parameters, and control the system to track the desired trajectory and suppress the elastic vibration preferably.