In this paper, we investigate the problem of trajectory tracking control for marine surface vehicles (MSVs), which are subject to dynamic uncertainties, external disturbances and unmeasurable velocities. To recover the unmeasurable velocities, a novel adaptive neural network-based (NN-based) state observer is constructed. To guarantee the transient and steady-state tracking performance of the system, a novel nonlinear transformation method is proposed by employing a tracking error transformation together with a newly constructed performance function, which is characterized by a user-defined settling time and tracking control accuracy. With the aid of the state observer and the nonlinear transformation method in combination with the adaptive NN technique and vector-backstepping design tool, an adaptive neural output-feedback trajectory tracking control scheme with predefined performance is developed. With regard to the developed control scheme, uncertainties can be reconstructed only by utilizing the position and heading of the MSVs. Independent designs of the state observer and the controller can be achieved, and the position tracking error can be guaranteed to fall into a predefined residual set in the user-defined time frame and remain in the above set. A rigorous stability analysis validates that all signals in the closed-loop trajectory tracking control system for MSVs are uniformly ultimately bounded. Simulation results verify the effectiveness of the developed adaptive neural output-feedback trajectory tracking control scheme.