In this paper, a phase-shifted full-bridge current-doubler synchronous rectifying converter (PSFB-CDSRC) based on IGBT and its control strategies are studied. In the main circuit, a current doubling synchronous rectifying circuit based on IGBT is presented to further reduce the power loss of power devices. Moreover, in the control strategy, in view of the existing researches, the basic BP neural network PID control performance of the rectifying converter still can be further improved. Therefore, this paper combines the quasi-Newton algorithm and traditional GA to propose an improved GA-BP (IGA-BP) neural network to further improve PID control performance. The simulation results demonstrate that the maximum efficiency of 5 V/500 A rectifying converter based on the proposed circuit scheme can reach 94.1%, and the rectifying converter has a good performance of excellent waveform and wide range of load. IGA-BP neural network PID control responds fast and reaches the stable state quickly in comparison with that controlled by the GA-BP neural network control strategy, and the steady-state time can be reduced by 10.5% through using IGA-BP neural network control strategy. This study can provide a valuable guidance and reference, not only in circuit scheme but also in the optimal PID control strategy for design of the high-efficiency DC/DC rectifying converter with higher power in the future.