The snow leopard (Panthera uncia) lives in alpine ecosystems in Central Asia, where it could face intensive climate change and is thus a major conservation concern. We compiled a dataset of 406 GPS-located occurrences based on field surveys, literature, and the GBIF database. We used Random Forest to build different species distribution models with a maximum of 27 explanatory variables, including climatic, topographical, and human impact variables, to predict potential distribution for the snow leopard and make climate change projections. We estimated the potential range shifts of the snow leopard under two global climate models for different representative concentration pathways for 2050 and 2070. We found the distribution center of the snow leopard may move northwest by about 200 km and may move upward in elevation by about 100 m by 2070. Unlike previous studies on the range shifts of the snow leopard, we highlighted that upward rather than northward range shifts are the main pathways for the snow leopard in the changing climate, since the landform of their habitat allows an upward shift, whereas mountains and valleys would block northward movement. Conservation of the snow leopard should therefore prioritize protecting its current habitat over making movement corridors.