Abstract: The operation of space flexible joint space manipulator relates to many factors. One of the key factors is the elastic vibration of the joints. A control strategy is introduced for the trajectory tracking of a twolink space flexible joint manipulator. The EulerLagrange formula is used for modeling the dynamics of the manipulator system. Then, a successive linearization model predictive control scheme is proposed for the tracking control of the space manipulator. Finally, some numerical simulation are carried out to validate the effectiveness of the proposed method.