Abstract: The dynamics modeling, motion trajectory tracking control and elastic vibration suppressing problems of free-floating space manipulator system with flexible joints, uncertain system parameters and external disturbances are studied. The system's dynamic equations are established by using the momentum conservation, angular momentum conservation and the Lagrange equation. According to the singular perturbation method, the system is decomposed into two independent subsystems: a slow subsystem (represents the system's rigid part) and a fast subsystem (represents the system's flexible part). For the slow subsystem, a robust backstepping control method based on a state observer is designed to eliminate the “rigid-flexible rotation angle error”, compensate the uncertain system parameters and the external disturbances, and achieve the asymptotic tracking of the space manipulator. During the control procedure, there is no need to measure and feedback the system's velocity signals by use of the state observer, so the control method is simpler and more precise. For the fast subsystem, a velocity difference feedback control method is used to stabilize the elastic vibrations caused by the flexible joints, and guarantee the system's stability. The simulation results prove the proposed control method's efficiency.