Climate change is amongst the main threats to biodiversity. Considering extant mammals endured Quaternary climate change, we analyzed the extent to which this past change predicts current mammals' extinction risk at global and biogeographical scales. We accessed range dynamics by modeling the potential distribution of all extant terrestrial mammals in the Last Glacial Maximum (LGM, 21,000 years ago) and in current climate conditions and used extinction risk from IUCN red list. We built General Linear Mixed-Effects Models to test the magnitude with which the variation in geographic range (ΔRange) and a proxy for abundance (ΔSuitability) between the LGM and present-day predicts current mammal's extinction risk. We found past climate change most strongly reduced the geographical range and climatic suitability of threatened rather than non-threatened mammals. Quaternary range contractions and reduced suitability explain around 40% of species extinction risk, particularly for small-bodied mammals. At global and biogeographical scales, all groups that suffered significant Quaternary range contractions now contain a greater proportion of threatened species when compared to groups whose ranges did not significantly contract. This reinforces the importance of using historical range contractions as a key predictor of extinction risk for species in the present and future climate change scenarios and supports current efforts to fight climate change for biodiversity conservation.