A $CO_2$ system using the two-stage compression cycle was tested by varying $1^{st}-2^{nd}$ compressor frequencies in the cooling mode. To improve the cooling performance of the two-stage compression $CO_2$ cycle, the following cycle options were applied: a basic cycle, a cycle with an intercooler, a cycle with an IHX (internal heat exchanger), and a cycle with an intercooler and IHX. The cycle with the intercooler-IHX showed the highest cooling capacity improvement among the cycle options at all compressor frequencies. The cycle with the intercooler, the cycle with the IHX, and the cycle with the intercooler-IHX improved the cooling COP by 7, 12, and 15%, respectively, over the basic $CO_2$ cycle when the compressor frequencies for the first and second compressors were 50 Hz and 30 Hz, respectively. In addition, the applications of the selected cycle options enhanced system reliability.