Drought is a natural phenomenon in which the natural amount of water in an area is below the normal level. It has negative impacts on production in numerous industries and people’s lives, especially in the context of climate change. Investigating the spatial–temporal variation of drought is of great importance in water resource allocation and management. For a better understanding of how drought has changed in China from 1961 to 2020 and will change in the future period of this century (2021–2100), a spatial–temporal assessment of drought based on the standardized precipitation evapotranspiration index (SPEI) was carried out. The trends and characteristics (number, duration, and severity) of historical and future droughts in China were evaluated based on 12-month SPEI by employing the Mann–Kendall test, Sen’s slope and run theory. The similarities, differences, and spatial–temporal evolution of droughts in these two periods were analyzed. The results showed that in the historical period the number of droughts decreased gradually from the south of China to the north. Less frequent drought but with longer duration and stronger severity occurred in the northeast and the northern areas. In the future period, most parts of China are projected to suffer more severe droughts with longer duration, especially for Northeast China, North China, Qinghai–Tibetan Plateau, and Southwest China. The likely increasing severity and duration of droughts in most areas of China in the future makes it very necessary to formulate the corresponding drought prevention and relief strategies to reduce the possible losses caused by droughts.