The effects of climate change on biodiversity should depend in part on climate displacement rate (climate-change velocity) and its interaction with species’ capacity to migrate. We estimated Late Quaternary glacial-interglacial climate-change velocity by integrating macroclimatic shifts since the Last Glacial Maximum with topoclimatic gradients. Globally, areas with high velocities were associated with marked absences of small-ranged amphibians, mammals and birds. The association between endemism and velocity was weakest in the highly vagile birds and strongest in the weakly dispersing amphibians, linking dispersal ability to extinction risk due to climate change. High velocity was also associated with low endemism at regional scales, especially in wet and aseasonal regions, where conditions otherwise favor high richness. Overall, we show that low-velocity areas are essential refuges for Earth’s many small-ranged species.