In this paper, the trajectory tracking control of underactuated autonomous underwater vehicle without measuring velocity in three-dimensional space and in the presence of unknown disturbances caused by waves and ocean currents is studied based on dynamic surface control for the first time. In order to estimate parametric uncertainties with underwater vehicle dynamic model, radial basis function neural network approximation technique has been proposed. Also, the output feedback control problem is resolved by employing a high-gain observer to estimate the required unmeasurable states. The stability of the proposed controller is investigated by an analysis based on Lyapunov theory and uniform ultimate boundedness stability of states and convergence of tracking errors to a small bound around the origin are guaranteed. Finally, the tracking performance of the proposed control scheme has been verified via computer simulations.