The isentropic exponent in the near-critical region can sharply change with operation condition transitions of a closed Brayton cycle, thus having significant impacts on the compressor aerodynamic performance and the internal flow of the compressor embedded into the cycle. This paper investigates the isentropic exponent effects of the supercritical carbon dioxide (CO2) using theoretical analyses and three-dimensional computational fluid dynamic (CFD) simulations. The theoretical analysis reveals that the increasing isentropic exponent mitigates the impeller work coefficient and the impeller outlet Mach number but raises the suction side Mach number of the impeller blade and blade loading at the leading edge. The CFD results provide validations for the theoretical results. Based on the findings, a suggestion is offered to guide the physical experiment design of a centrifugal compressor with supercritical CO2 as its working fluid.