Potential natural vegetation (PNV), the final successional stage of vegetation, plays a key role in ecological restoration, the design of nature reserves, and development of agriculture and livestock production. Meteorological data from historical and current periods including the last inter-glacial (LIG), last glacial maximum (LGM), mid Holocene (MH) periods and the present day (PD), plus derived data from 2050 and 2070, in conjunction with the Comprehensive and Sequential Classification System (CSCS) model, were used to classify global PNV. The 42 classes of global PNV were regrouped into 10 groups to facilitate analysis of spatial changes. Finally, spatio-temporal patterns and successional processes of global PNV as well as the response to climate changes were analysed. Our study made the following five conclusions. (1) Only one missing class (IA1 frigid-extrarid frigid desert, alpine desert) arose in periods of LIG, MH, 2050, and 2070 for global PNV. (2) The frigid-arid groups were mainly distributed in higher latitudes and elevations, but temperate-humid groups and tropical-perhumid groups occurred in middle and low latitudes, respectively. Temperate zonal forest steppe, warm desert, savanna and tropical zonal forest steppe increased, while six other groups decreased. (3) The conversion from temperate zonal forest steppe to tundra and alpine steppe from LIG to LGM occupied the largest area, indicating a drastic shift in climate and the associated response of terrestrial vegetation sensitive to climate change. (4) The CSCS could be used to simulate the long-term succession of global PNV. (5) As a consequence of global warming, forests shifted to the northern hemisphere and Tibet, areas with much higher latitude and elevation. The PNV groups with greater shift distance revealed the more serious effects of global climate change on vegetation.