The energy-stored quasi-Z-source inverter (ES-qZSI) has attracted much attention for photovoltaic (PV) power generations, due to its capability to stabilize the PV power fluctuations with simple structure and other advantages of Z-source inverter. The improved dual-mode (DM) ES-qZSI is able to support all-weather operation even at night or cloudy days when PV power is extremely low. Whereas, the traditional proportional-integral (PI) based control suffers from complicated controller design and poor dynamic response during mode transition, due to two sets of PI control required for the daytime and night operation modes. In order to overcome that, this paper proposes a model predictive control strategy for the DM-ES-qZSI PV power system. The system predictive models in both day and night operating modes are derived. The control strategy is disclosed to ensure high performance of the system, through calling the predictive models and defined cost functions of the two modes within a single control loop. Simulation and experiment are carried out to verify the effectiveness of proposed control strategy.