To understand the current biodiversity crisis, it is crucial to determine how humans have affected biodiversity in the past. However, the extent of human involvement in species extinctions from the Late Pleistocene onward remains contentious. Here, we apply Bayesian models to the fossil record to estimate how mammalian extinction rates have changed over the past 126,000 years, inferring specific times of rate increases. We specifically test the hypothesis of human-caused extinctions by using posterior predictive methods. We find that human population size is able to predict past extinctions with 96% accuracy. Predictors based on past climate, in contrast, perform no better than expected by chance, suggesting that climate had a negligible impact on global mammal extinctions. Based on current trends, we predict for the near future a rate escalation of unprecedented magnitude. Our results provide a comprehensive assessment of the human impact on past and predicted future extinctions of mammals.