This paper proposes a hierarchical image-based visual servoing (IBVS) strategy for dynamic positioning of a fully actuated underwater vehicle. In the kinematic loop, the desired velocity is generated by a nonlinear model predictive controller, which optimizes a cost function of the predicted image trajectories under the constraints of visibility and velocity. A velocity reference model, representing the desired closed-loop vehicle dynamics, is integrated with an IBVS kinematic model to predict the future trajectories. In the dynamic velocity tracking loop, a neural-network-based model reference adaptive controller is designed to ensure the convergence of the velocity tracking error in the presence of uncertainties associated with vehicle dynamic parameters, water velocity, and thrust forces. Comparative simulations with different control and system configurations are performed to verify the effectiveness of the proposed scheme and to illustrate the influences of the prediction horizon, cost function, closed-loop vehicle dynamics, and predictive velocity reference model on the IBVS system performance.