A scheme of fuzzy terminal sliding mode control was proposed for vibrat ion suppression of a flexible space manipulator base position of which was not c ontrolled. The dynamical equation of the flexible space manipulator was derived by using the assumed mode method, linear momentum conservation of the system and the Lagrange method. To solve the problems of trajectory tracking control and v ibration suppression of the flexible space manipulator, the singular perturbatio n approach was adopted to decompose the manipulator system into a slow subsystem and a fast subsystem. And then, the controller could be designed separately for the subsystems. A fuzzy terminal sliding mode control scheme was designed to co ntrol the slow subsystem and the linear quadratic regulator (LQR) based on the r educed order observer was proposed for the fast subsystem. A simulation example of flexible space manipulator demonstrates that the control scheme not only guar antees that the tracking errors of the base’s attitudes and arm’s joints of th e system converge to zero in finite time, but also weakens the chattering of the sliding mode controller and the vibration of the flexible arm effectively.