In order to solve the problem of high effective inductor current and peak value in the quadrilateral inductor current control strategy of four-switch Buck-Boost (FSBB) converter, a boundary conduction mode (BCM) control strategy was proposed, which shortened the freewheeling phase without power transmission to zero in the existing quadrilateral inductor current control strategy, so as to reduce the RMS and peak value of inductor current. Firstly, the current waveforms of the FSBB converter in different modes of working modes and inductor currents were analyzed. Secondly, the constraints of the FSBB converter to achieve soft switching under all working conditions were analyzed, and the value rules of the inductor current are obtained. Then, the variation of inductor current in different modes was analyzed, and the control method in critical continuous mode was given, when the input and output voltage difference was small, increase the output power by increasing the duty cycle of the first or third stage, and when the input and output voltage difference was large, the FSBB converter works in the critical continuous state of inductor current, which effectively reduces the effective value and peak value of inductor current. Finally, a simulation model was built. The results show that the proposed BCM control strategy can achieve zero-voltage turn-on and has good dynamic response ability.