In this paper, the depth control problem of autonomous underwater vehicles CAUVs) subject to multiple constraints is studied based on constrained model predictive control (MPC). In order to improve depth control accuracy under constraints, based on the derived dynamic model in discrete-time domain, the discrete state space expression of AUV is established, and a new constrained MPC control strategy is developed. In order to ensure the smoothness of depth tracking quadratic Bezier curve. Finally, simulation studies are conducted to demonstrate the effectiveness of the proposed constrained MPC solution.