Large herbivores are a major agent in ecosystems, influencing vegetation structure, and carbon and nutrient flows. During the last glacial period, a mammoth steppe ecosystem prevailed in the unglaciated northern lands, supporting a high diversity and density of megafaunal herbivores. The apparent discrepancy between abundant megafauna and the expected low vegetation productivity under a generally harsher climate with a lower CO2 concentration, termed the productivity paradox, requires large-scale quantitative analysis using process-based ecosystem models. However, most of the current global dynamic vegetation models (DGVMs) lack explicit representation of large herbivores. Here we incorporated a grazing module in a DGVM based on physiological and demographic equations for wild large grazers, taking into account feedbacks of large grazers on vegetation. The model was applied globally for present-day and the Last Glacial Maximum (LGM). The present-day results of potential grazer biomass, combined with an empirical land-use map, infer a reduction in wild grazer biomass by 79-93% owing to anthropogenic land replacement of natural grasslands. For the LGM, we find that the larger mean body size of mammalian herbivores than today is the crucial clue to explain the productivity paradox, due to a more efficient exploitation of grass production by grazers with a large body size.