Climate change is an important environmental issue that is causing global temperatures to rise. The primary environmental targets are to reduce carbon emissions and mitigate the impacts of climate change. The refrigeration system is a major emitter of greenhouse gases because it uses refrigerants with a high global warming potential. Due to its excellent thermophysical properties, the R134a is the most commonly used refrigerant in refrigeration systems; however, its high GWP will need to be disposed of earlier. To achieve global environmental objectives, conventional refrigerants need to be replaced with environmentally friendly and energy-efficient refrigerants. In the present work, a mathematical simulation has been carried out to check the performance of low-GWP refrigerant mixtures as environmentally friendly alternatives for R134a in a low-temperature system. In this study, a 190-L domestic refrigerator has been considered a low-temperature system. This simulation was performed using the MATLAB software, and the REFPROP database was used to obtain thermophysical properties of the refrigerants. The results showed that the COP of HFO mixtures decreased by 4-20% compared to R134a. The exergy efficiency of the R1234ze/R134a mixture improves by 4 to 16% as compared to the other mixtures and its performance is very similar to the R134a. Due to the environmentally friendly properties and flammability aspects, R1234ze/R134a (90/10) could be a good substitute for R134a in lower temperature applications and to satisfy the Montreal and Kyoto Protocol expectations.