In this paper, an adaptive trajectory tracking control algorithm for underactuated unmanned surface vessels (USVs) with guaranteed transient performance is proposed. To meet the realistic dynamical model of USVs, we consider that the mass and damping matrices are not diagonal and the input saturation problem. Neural networks (NNs) are employed to approximate the unknown external disturbances and uncertain hydrodynamics of USVs. Moreover, both full-state feedback control and output feedback control are presented, and the unmeasurable velocities of the output feedback controller are estimated via high-gain observer. Unlike the conventional control methods, we employ the error transformation function to guarantee the transient tracking performance. Both simulation and experimental results are carried out to validate the superior performance via comparing with traditional potential integral control approaches.