Abstract: The trajectory tracking control and the vibration suppression of a free floating space-based manip-ulator with elastic base are discussed in this paper. According to the geometric feature and the momentum conservation, the generalized Jacobian matrix is derived, And the Lagrangian method and the momentum con-servation are adopted in building the dynamic equations. Based on the results and under the assumption of two kinds of time scale, a singular perturbation model of the free floating space manipulator system is built. The slow-subsystem describes the tracking control of rigid motion while the fast-subsystem describes the vibration of elastic base. The computed torque control of the free floating space-based robot with elastic base is designed for the low-subsystem. The linear-quadratic optimal control is designed for the fast-subsystem. The simulation results show that the proposed control scheme is feasible for the tracking control and the vibration suppression.