In this paper, a carbon dioxide trans-critical refrigerating system which is different from a conventional subcritical refrigerating cycle was studied. The trans-critical carbon dioxide refrigerating systems are based on the Gustav Lorntzen cycle. Emphasis was focused on how to determine the optimal discharge pressure of compressor in CO2 trans-critical cycle. The factors related with the optimal discharge pressure were analyzed. A formula was developed based on cycle simulation, which could be used to predict the optimal discharge pressure of a basic CO2 trans-critical cycle. After further studies on CO2 trans-critical cycles with a regenerator or expander, two more formulas were also developed. These formulas could provide an access to improve the COP of CO2 trans-critical cycle. In this paper, a carbon dioxide trans-critical refrigerating system which is different from a conventional subcritical refrigerating cycle was studied. The trans-critical carbon dioxide refrigerating systems are based on the Gustav Lorntzen cycle. Emphasis was focused on how to determine the optimal discharge The factors related with the optimal discharge pressure were analyzed. which could be used to predict the optimal discharge pressure of a basic CO2 trans-critical cycle. After further studies on CO2 trans-critical cycles with regenerator or expander, two more formulas were also developed. These formulas could provide access to improve the COP of CO2 trans-critical cycle.