To achieve the optimal comprehensive efficiency of hybrid amphibious vehicle, a power coordinated predictive control strategy is proposed. This strategy deals with the coupling relationship between energy management strategy and longitudinal control strategy through collaborative optimization. Aiming at the mismatch of prediction model, an extreme learning machine (ELM) is used for real-time error prediction, and the prediction model is corrected through the predicted value. A model predictive controller (MPC) is designed for the real-time optimal control of energy management and longitudinal control, and it is verified by simulation. The results show that, compared with the traditional energy management strategy based on MPC, the proposed strategy can be used to reduce the equivalent fuel consumption, state-of-charge (SOC) standard deviation, bus voltage standard deviation and battery capacity fading by 9.35%, 59.63%, 15.79% and 45.33%, respectively. By comparing the power coordinated predictive control with and without model correction, it shows that the equivalent fuel consumption, SOC standard deviation, bus voltage standard deviation and battery capacity fading can be reduced by 6.95%, 25.91%, 13.46% and 24.07%, respectively, through model correction, which reflects the superiority of the power coordinated predictive control based on ELM model correction in improving the fuel economy, maintaining the stability of electrical system and reducing the battery consumption.