In the presence of uncertain dynamic terms and external disturbances, the problem of trajectory tracking with application to an underactuated underwater vehicle is addressed in this paper. Based on Lyapunov theory and properties of neural networks, a nonlinear neural controller is designed, where multilayer neural networks are adopted to approximate the unmodeled dynamic terms and external disturbances. In order to confine the values of estimated weights within predefined bounds, smooth projection functions are employed. Moreover, measurement noises are considered so as to simulate realistic operation scenario, while filters are designed to get cleaner states. From the stability analysis, it is proven that the tracking errors are globally uniformly ultimately bounded. Numerical examples are provided to demonstrate the robustness of the controller in the presence of unmodeled terms, disturbances and measurement noises.