In this paper, cycle performance analysis of R744($CO_2$) two-stage compression and one-stage expansion refrigeration system is presented to offer the basic design data for the operating parameters of the system. The operating parameters considered in this study include superheating degree, compressor efficiency, gas cooling pressure, mass flowrate ratio, outlet temperature of gas cooler and evaporating temperature in the carbon dioxide two-stage refrigeration cycle. The main results were summarized as follows : The cooling capacity of two-stage compression and one-stage expansion refrigeration system increases with the increasing superheating degree, compressor efficiency and gas cooling pressure, but decreases with the increasing mass flowrate ratio and evaporating temperature. The compression work of two-stage compression and one-stage expansion refrigeration system increases with the increasing superheating degree, outlet temperature of gas cooler, gas cooling pressure and evaporating temperature, but decreases with the increasing compressor efficiency and mass flowrate ratio. The COP of two-stage compression and one-stage expansion refrigeration system increases with the increasing compressor efficiency, but decreases with the increasing superheating degree, gas cooling pressure, mass flowrate ratio and evaporating temperature. Therefore, superheating degree, compressor efficiency, gas cooling pressure, mass flowrate ratio, outlet temperature of gas cooler and evaporating temperature of R744($CO_2$) two-stage compression and one-stage expansion refrigeration system have an effect on the cooling capacity, compressor work and COP of this system.