Abstract: The coordinated motion control and flexible vibration suppression problems of flexible space manipulator are studied. With the assumed mode method and the linear momentum conservation of the system, the system dynamics model of the space manipulator is derived. Based on the hybrid sliding mode concept, an adaptive variable structure control scheme is proposed for the flexible space manipulator to achieve the coordinated motion between the base's attitude and the arm's joints, which accounts for the uncertainty in inertial parameters. The hybrid sliding mode introduced consists of two parts, the frequency shaped optimal sliding mode and the terminal sliding mode. The former is used to suppress the vibration of flexible link of the system, and the latter is utilized to guarantee the convergence of system tracking errors in finite time. Moreover, the control scheme proposed does not require the foreknowledge of flexible variables in control. Thus, it can effectively avoid the real-time measurements and feedbacks of system flexible variables, and be more suitable for practical applications. Simulation results demonstrate the effectiveness of the proposed control scheme.