The Caribbean fruit fly, Anastrepha suspensa (Lower, 1862) (Diptera: Tephritidae), is a pest of significant economic importance in Central America and Florida (USA). This study was carried out to examine the influence of climate change on the space-time distribution of A. suspensa on temporal and spatial scales. The CLIMEX software was used to model the current distribution and for climate change. The future distribution was performed using two global climate models (GCMs), CSIRO-Mk3.0 (CS) and MIROC-H (MR), under the emission scenarios (SRES) A2 and A1B for the years 2050, 2080, and 2100. The results indicate a low potential for global distribution of A. suspensa in all scenarios studied. However, tropical areas were identified with high climatic suitability for A. suspensa in South America, Central America, Africa, and Oceania until the end of the century. Projections of areas with climatic suitability for A. suspensa can provide helpful information to develop preventive strategies of phytosanitary management avoiding economic impacts with the introduction of the species.