The battery energy stored quasi‐Z‐source (BES‐qZS) based photovoltaic (PV) power generation system combines advantages of the qZS inverter and the battery energy storage (BES) system. To realize multi‐objective cooperative control, a model predictive control (MPC) strategy for the PV grid‐connected system based on an energy‐storage quasi‐Z source inverter (ES‐qZSI) is proposed. The energy storage battery is added to the traditional quasi‐Z source inverter (qZSI). The MPC strategy is adopted to realize maximum power point tracking (MPPT), battery, and point of common coupling (PCC) tripartite energy control in a single‐stage conversion system. The discrete‐time model of ES‐qZSI is derived, and the cost function was constructed by using the system state variables. The PV power MPPT module, the battery power management module, and the PCC power module are designed to generate the reference signal of the prediction function. Finally, the proposed algorithm was validated by simulation. The theoretical analysis and simulation results were consistent.