In the field of high voltage and large capacity renewable energy grid connection system, electric machine variable frequency drive system, five-level converter has been received more and more attention. The five-level active neutral point clamped topology is evolved from the active neutral point clamped three-level structure and flying capacitor structure. It has simple structure and flexible control, which is the future development direction. For the three-phase five-level neutral point clamped grid-connected inverter, this paper proposes a spatial domain subdivision optimization based model predictive control strategy. With the control objectives of output current control, neutral point potential control, voltage control of suspended capacitor and switch state switching limitation, the small sector which the reference voltage vector is located, is determined in advance in the 60 degree angle coordinate system of space, and the voltage vector of the small sector is used for rolling optimization and iterative optimization of model predictive control, which greatly reduces the calculation time while achieving high-performance control. Simulation results verify the effectiveness of the proposed control algorithm.