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Numerical study on the compressor stage of a KJ-66 micro gas turbine was conducted in this paper through both steady and unsteady Reynolds-averaged Navier–Stokes. The study was conducted for the numerical prediction of micro gas turbine compressor performance at various operation conditions, with special attention given to the transient flow behaviors during compressor operation. The numerical results showed reasonable agreements with experimental data while providing predictions for the charting of compressor performance map at various operation speeds. The simulation results indicated that the increase of operation speed from 80 k r/min to 117 k r/min would leads to an increased peak total pressure ratio from 1.54 to 1.96, while decreasing the peak adiabatic efficiency from 0.73 to 0.55. This paper also provided discussion on details of transient flow field within the compressor stage as well as demonstrated the smooth flow transition through rotor–stator interactions.