Because of the limitations of traditional refrigerants, the application of trans-critical CO₂ technology in domestic gas conditioners and other fields is becoming increasingly popular. This paper proposes a new CO₂ trans-critical refrigeration system. Combining the internal heat exchanger and expander components, as well as the two-stage compression cycle, we analyzed the effectiveness of the expander, internal heat exchanger, and intercooling on system performance under various operating conditions in terms of energy, exergy analysis, and optimal discharge pressure. The system performance can be changed by changing the cycle conditions and internal heat exchanger effectiveness, which reduces system power consumption and the percentage of exergy losses of gas cooler components. Compared to the single-stage compression with expander cycle, the systems cycle power consumption is reduced by 2–15.7% and the maximum system COP is increased by 2.93–6.93%. From the view of energy effectiveness, the system’s maximum COP increases by 3.9% and the percentage of exergy losses of gas cooler decreases by 22.5% with the effectiveness of internal heat exchanger varying. The addition of an internal heat exchanger has resulted in improved system performance, which is important for providing a relevant cycle model for the application.