Abstract: In this paper, the control problem of free-floating space robot system with prismatic joints is studied. In order to overcome the difficulty that the dynamic equation of the system cannot be linearly parameterized, the space robot system is modeled as an under-actuated robot system. Thus, the system dynamic equation can be linearly parameterized. With the momentum conservation of the system, the kinematics of the system is analyzed, and it is shown that the generalized Jacobi matrix can also be linearly dependent on a group of inertial parameters. Based on the results proposed above, a robust and adaptive composite control scheme for the endeffector to track the desired trajectory in inertia space is proposed. The control scheme avoids measuring the position, velocity and acceleration of the base with respect to the orbit, because of an effective exploitation of the particular property of the system dynamics. Besides, the proposed control scheme is computationally simple, because the controller is robust to the uncertain inertial parameters. The control scheme is verified in a simulation study.