In this paper, we aim to address the trajectory tracking control problem for the unmanned surface vehicle (USV) subject to uncertain dynamics and unknown exogenous time-varying disturbance, in the presence of user-specified per-formance constraint. To improve the tracking accuracy, an uncertainty and disturbance estimator (UDE) is designed for compensating the uncertain hydrodynamic damping effect re-sulting from the inaccurate system modeling and the unknown external disturbance induced by the wind, wave, and ocean currents. To promote the tracking rapidity, the tracking error is confined within the prescribed region constructed by the upper and lower exponentially decaying functions. By incorporating the UDE and prescribed performance control technique, an accurate and rapid trajectory tracking control protocol is developed, whose implementation cost is low due to the removing of parameter update law. Simulation is carried out to demonstrate the performance of the developed UDE-based tracking control scheme.