The four-switch Buck-Boost (FSBB) converter can produce voltage conversion within a wide input voltage range, which is suitable for variable-speed permanent magnet synchronous generator (PMSG) energy storage systems with AC inputs and DC outputs. To reduce the interference of input voltage fluctuation on the performance of the FSBB converter, an input voltage feedforward (IVFF) compensation method is proposed in this paper. The switching synchronization strategy is simple. Using the switching average model, the small signal model of a non-ideal FSBB converter in all working modes is established. The effects of input voltage, load current, damping coefficient and right half plane (RHP) zero on the stability of the control system are analyzed in detail. The transfer function of the IVFF of the FSBB converter is derived, and the relationship between input voltage, load current and duty cycle is analyzed. Finally, the design of the parameters of the converter control system is presented. The simulation and experimental results show that this FSBB converter has high efficiency and a good transient response.