This study presents a comprehensive comparative analysis of the thermodynamic performance of a single-stage Linde-Hampson refrigerator (LHR) for refrigerant couples, namely R1234yf + R170, R1234yf + R23, R1234yf + R41 and R1234yf + R1132a, to seek the most suitable substitute for R23 at the temperatures down to −60 °C. The compressor input power, cooling capacity, coefficient of performance, exergy loss and exergy efficiency are selected as the objective functions. The operating parameters include the evaporation temperature, suction pressure, and condenser outlet temperature. The compositions of each binary mixture were obtained from the vapor-liquid equilibrium behavior according to the suction pressure and target evaporation temperature. Simulation and comparative study show that better energy and exergy performance are obtained with all the replacements under all studied conditions compared to R23. Further results show that the R1234yf + R41 mixture performs better, and hence is suggested as the most promising alternative couple for the single-stage LHR at −60 °C. By properly increasing the suction pressure and decreasing the condensation temperature, the system performance can be enhanced. This indicates that a multi-objective scheme has the potential to significantly improve the performance of low-temperature applications.