In this paper, a variable structure controller with time-varying sliding surface is proposed for robot manipulators. The proposed time-varying sliding surface ensures the ezistence of sliding mode from an initial state, while the conventional sliding surface cannot achieve the robust performance against parameter variations and disturbances before the sliding mode occurs. Therefore, error transient can be fully prescribed in advance for all time. Furthermore, it is shown that the overall system is globally ezponentially stable. The eficiency of the proposed method for the trajectory tracking has been demonstrated by simulations.