Warming and drought pose a serious threat to tropical forest. Yet the extent of this threat is uncertain, given the lack of methods to evaluate the forest tree cover changes under future climate predicted by complex dynamic vegetation models. Here we develop an empirical approach based on the observed climate space of tropical trees to estimate the maximum potential tropical tree cover (MPTC) in equilibrium with a given climate. We show that compared to present-day (2000-2009) conditions, MPTC will be reduced by 1 to 15% in the tropical band under equilibrium future (2090-2099) climate conditions predicted by 19 IPCC climate models. Tropical forests are found to regress or disappear mainly in the current transition zones between forest and savanna ecosystems. This climate pressure on tropical forests, added to human-caused land use pressure, poses a grand challenge to the sustainability of the world's largest biomass carbon pool.