Given the low output voltage of new energy systems, such as fuel cells or wind power, this paper proposes a high gain and high efficiency DC converter with fitting explicit model predictive control (MPC). The converter has the basic unit structure of non-isolated three-winding coupled inductor. By changing the turns ratio, this not only achieves higher voltage gain with the appropriate duty cycle, but also reduces the switching device stress. In addition, a passive clamp circuit is adopted to recycle the leakage inductance energy and suppress the voltage spike of the switch. To improve the dynamic performance and immunity of the proposed converter, the strategy of offline fitting of explicit MPC control law of a neural network is used to improve the output voltage tracking accuracy, and reduce the disturbance caused by variational input voltage and load, achieving good dynamic response. Finally, based on theoretical analysis, a prototype with input of 10~12 V and output of 100 V/100 W is built to verify the effectiveness of the proposed converters.