In this study, a two-stage phase-separate cycle was investigated analytically to improve the performance of the $CO_2$ system in the cooling mode. The simulation results were verified with the measured data. The predictions using the simulation model were consistent with the measured data within ${pm}20%$ deviations. The performance of the modified $CO_2$ system with the two-stage phase-separated cycle was analyzed with the variations of outdoor temperature and EEV opening. The cooling COP decreased with the increase of compressor frequency. The highest COP was 2.7 at compressor frequencies of 30 Hz and 30 Hz for the first and second compressors, respectively. In addition, the cooling COP increased by 9.3% with an application of optimum control of the first and second-stage EEV openings.