In order to maintain the high efficiency operation of the LLC resonant converter, the LLC resonant converter usually works near the resonant frequency, which makes the converter gain range narrow. To address this problem, this paper proposes a topology of primary-side Buck-LLC cascade converter and secondary-side special full-bridge rectifier, which is capable of realizing a wide range of voltage gains. The primary side of this topology adopts a synergistic control strategy of the front-stage Buck unit control and the back-stage LLC resonant converter, Namely, the front-stage realizes the closed-loop voltage stabilization function by PWM modulation, and the back-stage adopts the open-loop of the LLC to work at the point of resonance frequency. The overlapping conduction control method is introduced at the vice-side, and the voltage gain is adjusted by adjusting the overlapping duty cycle of the rectifier bridge switching tubes, so that the system can automatically switch the operation mode according to the output voltage, and the system can realize a 3-fold gain extension range. Theoretical derivation shows that all switching tubes of the system realize soft switching in a wide gain range. Combined with the state plane trajectory diagram, the voltage gain equation and soft-switching boundary conditions are derived. To validate the proposed scheme, an experimental prototype with DC300 V input and DC20-60 V/500 W output is built, and the experimental results and analysis verify the correctness and effectiveness of the system topology and control strategy.