The performance and efficiency of a centrifugal compressor are usually affected by the highly complex 3-dimensional flow structures which develop in the flow field of the compressor. Several experiments and research using numerical analysis have been reported, however, there are still many unknown physical phenomena that need to be studied, in order to optimize the design and improve the efficiency of turbomachines, especially those installed on hydrogen-powered fuel cell electric vehicles (FCEVs). In this study, the 3-dimensional vortex structures were analyzed using the critical-point theory and the probabilistic definitions, for an air supply device mounted on the commercial hydrogen FCEVs. The behavior of the complex 3-dimensional vortex structures at the design flow rate and low flow rate were elucidated. A tip leakage vortex was observed to develop at the leading edge of the main blade at all flow rates, which caused interference to the splitter blade. At 60% of the design flow rate, a vortex breakdown occurred at the tip leakage vortex near the leading edge of the main blade, and a reverse flow at 50% chord length of the main blade’s suction surface. The boundary layer which developed at the leading edge of the main blade’s suction surface at all flow rates led to the creation of a hub separation vortex by interfering with the boundary layer developed at the hub surface as a result of the centrifugal force. In addition, the boundary layer developed at the hub and shroud surface created a horseshoe vortex as it moved downstream and interfered with the leading edge of the main blade and splitter blade. It was confirmed that the behavior of the tip leakage, hub separation, and horseshoe vortex structures determined the aerodynamic performance of the centrifugal compressor. The average pressure difference improved by 1.47% of the entire flow rate after optimizing the compressor design.