Interleaved parallel buck converter in charging new energy lithium battery, often use the traditional PI control first to the lithium battery constant current charging (CC) and then to the lithium battery constant voltage charging (CV). The traditional PI control has the disadvantages of slow response, poor inductor current equalization, and large output current and voltage ripple. Thus, by analyzing the circuit model of four-phase interleaved parallel converter, an inductor current control strategy of MPC is proposed. Firstly, a prediction model is established, a cost function is constructed to find the optimum, and the entire converter is controlled accordingly. Because MPC has good dynamic response characteristics and can make the four branches of the converter inductor current to achieve good equalization effect, using its characteristics combined with the output current outer loop or voltage outer loop PI control, so that the output current or voltage also has good dynamic response, can also make the four branches of the inductor current to achieve good equalization effect. And because there is a process of switching constant-current mode to constant-voltage mode for Li-ion battery charging, making the output prone to overshoot when switching, so a control strategy is proposed to inherit the PI outer loop on the integral amount when switching, i.e. inherited PI-MPC. Finally, the simulation experiment verifies that the inherited PI-MPC can make the output ripple smaller and keep the inductor current well equalized compared with the traditional PI control.