To address the issues of small and nonlinear output voltage of proton exchange membrane fuel cells, which are susceptible to polarization losses, load fluctuations and insufficient stability when cooperating with Boost converter, this study was conducted. Firstly, a PEMFC output voltage model including three types of polarization losses (activation, ohmic and concentration polarization) and a state-space average model of the Boost converter were constructed. Then, the output function was reconstructed to meet the conditions of feedback linearization, and an inversion sliding mode controller with an adaptive reaching law was designed to suppress chattering. Finally, based on Matlab/Simulink simulation, the performance of BSMC was compared with that of PI control. The results show that the steady-state voltage error rate of BSMC is 0.099% (0.170% for PI control), its dynamic response is 20.1%~34.1% faster, and its voltage drop amplitude and recovery time are superior to those of PI control under disturbance. The results indicates that this strategy can improve the PEMFC voltage control efficiency under complex working conditions and provide theoretical and technical support for its stable operation.