Three-stage vapor compression refrigeration systems (TSVCRS) are extensively preferred for very low temperature refrigeration applications due to the limitation of low volumetric efficiency of compressors in a single stage. In this paper, the thermodynamic analysis of TSVCRS is presented using R744, R717, and R410A in the LTC (low-temperature cycle), MTC (medium-temperature cycle), and HTC (high-temperature cycle) at the base case. It is observed that the overall COP of TSVCRS increases with an increase in cascade condensing temperatures of LTC and MTC up to a certain limit of −43.33℃ at LTC and −7.22℃ at MTC, then starts decreasing. Thus, the optimum condensing temperature is a subtle design parameter for the performance of TSVCRS. The maximum COP at these optimum condensing temperatures of LTC and MTC are estimated to be 0.716. These optimum values are further estimated using different combinations of refrigerants in LTC, MTC, and HTC. The potential candidates considered in present study are R744, R170, R1150 (LTC); R717, R290, R717 (MTC) and R410A, R1234yf, R600 (HTC). These alternative refrigerants are selected based on their commercial viability under the given temperature and pressure range. The system predicts the highest COP of 0.763 using R744, R290, and R410A in LTC, MTC, and HTC, respectively. Further, the optimum condensing temperature of LTC and MTC at this operating point is −47.22℃ and −6.22℃, respectively.