The smoke tree (Cotinus coggygria Scop.) is a woody species widely distributed in the Mediterranean region and East Asia, and it has high ecological, ornamental, and economic value. Investigating changes in the suitable habitat in different historical periods and under climate change in the future can provide key insights for understanding and projecting changes in the distribution of Cotinus species. In this study, we used a MaxEnt model to simulate the current, historical and future suitable habitat for C. coggygria based on distribution records of wild C. coggygria and environmental variables. The results showed that C. coggygria had an East Asian-Tethyan disjunction, and the suitable habitat was most affected by temperature and precipitation. At the Last Glacial Maximum, C. coggygria in the Mediterranean retreated to glacial refugia in southern Europe and survived in situ in East Asia. Under future climate scenarios, the suitable habitat of C. coggygria gradually expanded northward. As emission levels increased, the suitable habitat for C. coggygria expanded northward. The overall suitable habitat in the future was larger in the Mediterranean than in East Asia; however, the highly suitable habitat was less in the Mediterranean than in East Asia. The suitable habitat in the Mediterranean was greatly affected by different scenarios, but this was not the case in East Asia. The results of this study explored the effects of climate, soil, and topographic variables on the suitable habitat for C. coggygria and changes in the suitable habitat under historical and future climatic situations. Our findings will aid the conservation and cultivation of C. coggygria, as well as studies of species with discontinuous distributions in Eurasia.