The explicit model predictive control (MPC) can solve the piecewise control laws offline to save online implementation burden. However, many offline control laws have to be stored to adapt the operating point variation, the correct control law needs to be searched, and the control parameter needs to be calculated. The large storage and computational burdens make the explicit MPC difficult to be applied to the scenarios with high switching and control frequencies. To solve these problems, this article proposes to utilize a backpropagation neural network (BPNN) to fit the input-output relationship of the offline control laws under different operating points. It not only guarantees the control performance but also reduces the storage and computational burden. Such a BPNN method directly calculates the control parameter in a parallel way and thus eliminates serial evaluation of the searching process. Simulation results are provided and compared with the state-of-the-art controls to show the effectiveness of the proposed method. Experimental results demonstrate that a BPNN with 49 parameters can fit more than 10 000 offline control laws, and its implementation can be completed within three clock cycles by field-programmable gate array (FPGA) or application-specific integrated circuit (ASIC), so the 1-MHz switching and control frequency can be achieved with 4-MHz clock frequency.