Distributed generation (DG) has been widely used in low and medium-voltage applications. The need for high step-up DC-DC converters continues to increase. A novel single input dual output (SIMO) high step-up DC-DC converter is proposed. This converter adds a capacitor and diode to form a polarity reverse pole based on the traditional Boost circuit, and the power ports are interconnected through differential connection, improving the voltage gain of the converter and reducing the voltage stress of the switch. At the same time, port power control is independent, further improving the flexibility of power routing. The circuit structure and working principle of the converter are analyzed in detail, and expressions for voltage gain, electrical stress of main switching devices, and current ripple in steady-state are derived. Then, a vector-based time model predictive control strategy is proposed, a predictive model of the converter is established, the vector time of the switch is derived, and the optimization process of the objective function is designed. Finally, the feasibility of the proposed converter and the effectiveness of the control strategy are verified through simulation and experiment. The higher efficiency and lower voltage stress of semiconductors are also verified.