Abstract: Aiming at the problems of high backflow power, slow dynamic response and weak robustness of hybrid three-level dual active bridge direct current direct current(DC-DC) converters under extended phase shift control, a hybrid control strategy based on output voltage dynamic matrix control and Karush-Kuhn-Tucker(KKT) condition is proposed to optimize backflow power. The mathematical model of transmission power is established and the characteristics of reflux power are analyzed, and the optimal combination of phase shift ratio to achieve the minimum backflow power in different operating modes is derived. The realization process of dynamic matrix control voltage prediction is described from three steps of prediction model, rolling optimization and feedback correction, so as to improve the dynamic performance of the system. Finally, compared with the traditional extended phase shift control and transmission power error minimization control, the simulation and experimental results show that the proposed control strategy can optimize the reflux power in the full power range, and also improve the dynamic response performance of the converter, which verifies the correctness and effectiveness of the proposed method.