Glutathione peroxidase-like enzyme is an important enzymatic antioxidant in plants. It is involved in scavenging reactive oxygen species, which can effectively prevent oxidative damage and improve resistance. GPXL has been studied in many plants but has not been reported in potatoes, the world’s fourth-largest food crop. This study identified eight StGPXL genes in potatoes for the first time through genome-wide bioinformatics analysis and further studied the expression patterns of these genes using qRT-PCR. The results showed that the expression of StGPXL1 was significantly upregulated under high-temperature stress, indicating its involvement in potato defense against high-temperature stress, while the expression levels of StGPXL4 and StGPXL5 were significantly downregulated. The expression of StGPXL1, StGPXL2, StGPXL3, and StGPXL6 was significantly upregulated under drought stress, indicating their involvement in potato defense against drought stress. After MeJA hormone treatment, the expression level of StGPXL6 was significantly upregulated, indicating its involvement in the chemical defense mechanism of potatoes. The expression of all StGPXL genes is inhibited under biotic stress, which indicates that GPXL is a multifunctional gene family, which may endow plants with resistance to various stresses. This study will help deepen the understanding of the function of the potato GPXL gene family, provide comprehensive information for the further analysis of the molecular function of the potato GPXL gene family as well as a theoretical basis for potato molecular breeding.