Tomato red spider mite Tetranychus evansi Baker and Pritchard (Acari:Tetranychidae) is a phytophagous pest that causes severe damage to Solanaceous plants worldwide, resulting in significant economic losses. In this study, the maximum entropy model was used to predict the potential current (1970–2000) and future (2021–2060) global distribution of the species based on its past occurrence records and high-resolution environmental data. The results showed that the mean values of the area under the curve were all >0.96, indicating that the model performed well. The three bioclimatic variables with the highest contributions were the coldest quarterly mean temperature (bio11), coldest monthly minimum temperature (bio6), and annual precipitation (bio12). A wide range of suitable areas was found across continents except Antarctica, both currently and in the future, with a much larger distribution area in South America, Africa, and Oceania (Australia), dominated by moderately and low suitable areas. A comparison of current and future suitable areas reveals a general trend of north expansion and increasing expansion over time. This study provides information for the prevention and management of this pest mite in the future.