Air compressors in hydrogen fuel cell vehicles play a crucial role in ensuring the stability of the cathode air system. However, they currently face challenges related to low efficiency and poor stability. To address these issues, the experimental setup for the pneumatic performance of air compressors is established. The effects of operational parameters on energy consumption, efficiency, and mass flow rate of the air compressor are revealed based on a Morris global sensitivity analysis. Considering a higher flow rate, larger efficiency, and lower energy consumption simultaneously, the optimal operating combination of the air compressor is determined based on grey relational multi-objective optimization. The optimal combination of operational parameters consisted of a speed of 80,000 rpm, a pressure ratio of 1.8, and an inlet temperature of 18.3 °C. Compared to the average values, the isentropic efficiency achieved a 48.23% increase, and the mass flow rate rose by 78.88% under the optimal operational combination. These findings hold significant value in guiding the efficient and stable operation of air compressors. The comprehensive methodology employed in this study is applicable further to investigate air compressors for hydrogen fuel cell vehicles.