Abstract: model predictive control (MPC) algorithm is proposed. Firstly，establish the kinematic and dynamic equations of the underwater vehicle and convert them into discrete system state space equations；Then，considering the influence of uncertain parameters such as water flow velocity，the recursive least squares algorithm is used to identify the uncertain parameters；Finally，design a controller for adaptive MPC algorithm to predict and control the trajectory of underwater vehicles with uncertainty，and verify it in a simulation environment. The results show that the average root mean square error of this method in sinusoidal trajectory tracking of underwater vehicles is about 0.5%；In the Z-shaped trajectory tracking of underwater vehicles，the average root mean square error is about 1%，which has higher control accuracy compared to MPC algorithm designed controllers and mainstream control methods. From this，it can be concluded that this method can improve the accuracy of trajectory prediction control for underwater vehicles with uncertainty，providing a reference for achieving more accurate and stable trajectory prediction control for underwater vehicles.