Unmanned Surface Vessels(USV) with only surge force and yaw moment available are typical under actuated system which cannot be stabilized by any time-invariant continuous state feedback control law. For the realistic underactuated USV, where the mass and damping matrices are not diagonal, based on additional controller and backstepping method, a smooth time-varying tracking controller is developed to track any straight and curved reference trajectories, and also confines the transient response performance within the allowable range. Firstly, the system is converted into a diagonal form by using state transformations and control input is simplified through feedback linearization theory. Secondly, the virtual controller is designed to stabilize tracking error, meanwhile, Barrier-Lyapunov Function(BLF) is introduced to ensure that the tracking error does not exceed the prescribed value. Thirdly, the additional control is designed to deal with the problem of underactuation. Stability analysis shows that the proposed control strategies can guarantee all the states in the closedloop system are uniform ultimate bound. Matlab/Simulink results illustrate the effectiveness of the proposed control design.