Abstract: In this paper, the control problem of free-floating space manipulator system with prismatic joint was studied. It is shown that the Jacobian matrix and the dynamic equations of the system could not easily be linearly parameterized, if we deduced it by use of the conservation relationship of the momentum and the angular momentum of the system. With the augmentation approach, we got the augmented generalized Jacobi matrix and the dynamic equation of the system that could be linearly dependent on a group of inertial parameters. Based on the results, the composite adaptive control scheme for free-floating space manipulator system with prismatic joint and unknown inertial parameters to track the desired trajectory in inertia space is proposed. The advantages of the control scheme proposed are that it needs not to measure the position, velocity and acceleration of the base. A two-link planar space manipulator system is simulated to verify the proposed control scheme.