Proton Exchange Membrane Fuel Cell (PEMFC) is a very attractive power source to meet high efficiency and low emission. For mobility applications, PEMFC needs to have a larger power density and it can be achieved with an air compressor to intake more air for chemical reaction. Different from a turbocharger, the compressor for PEMFC is not driven by a turbine, but by an electric motor as well. Due the limitation of motor speed and compact system size, the air compressor must be in small size and operate with low rotational speed. In compressor aerodynamic study, low specific speed and small size is believed to have large loss and it needs to be further investigated and improved. In this paper, a centrifugal compressor combined with an air bearing is specially developed, with rotational speed as 120k RPM and pressure ratio as 3.5. The compressor impeller, diffuser and volute are designed by mean-line method followed by 3D detailed design. Computational fluid dynamics method is employed to predict compressor performance as well as analyze compressor internal flow field and loss mechanism. Simulation results indicate that major losses including leakage flow loss in impeller and loss in diffuser. As a result, corresponding optimization design method is proposed, the total-to-total aerodynamic efficiency of the redesigned compressor has increased 5% at design point.