In the navigation of underwater robots, large ocean current disturbance often causes significant tracking errors. To better resist ocean current disturbance, the hydrodynamic characteristics of the spherical underwater robot are studied, and a model predictive control strategy based on adaptive model parameters is proposed, according to these characteristics. Firstly, the hydrodynamic characteristics of the robot under static water and constant flow disturbance were obtained and analyzed by the computational fluid dynamics method. Then, the dynamic models of the robot under different disturbances could be calculated from the data obtained, based on the least square method. Finally, an adaptive model predictive control (AMPC) strategy, with an ocean current observer, was designed, based on the dynamic models. When the current disturbance velocity was twice the robot velocity, the proposed strategy reduced the tracking error by 39% and 42% in X and Y directions, respectively. In addition, the hydrodynamic characteristics were verified by experiments.