The paper aims to solve the problems of negative-sequence and zero-sequence current of the three-phase four-wire power distribution system under three phase unbalance of a power grid. A model predictive current control strategy is proposed which chooses a capacitor split converter as the research object. First, a prediction model of the inverter output current under aβ0coordinates is constructed via coordinate transformation. Secondly, the zero-sequence reference current is calculated directly using a reference compensation component detection method based on instantaneous reactive power theory. Finally, the different voltage vectors output by the inverter are evaluated by applying the value function. The optimal voltage vector which makes the value function a minimum is selected and then applied to the next sampling period to realize target current compensation. The proposed control strategy effectively reduces the three-phase unbalance of the power grid, compensates the zero-sequence current generated by three-phase load imbalance, and improves the power quality of the power grid and system operation performance. The simulation and experimental results show the effectiveness of the proposed control strategy under power grid imbalance. This work is supported by Youth Science Fund of National Natural Science Foundation of China (No. 51607159 and No. 51707176).