Vegetation reconstructions from pollen data for the Last Glacial Maximum (LGM), 21 ky ago, reveal lanscapes radically different from the modern ones, with, in particular, a massive regression of forested areas in both hemispheres. Two main factors have to be taken into account to explain these changes in comparison to today's potential vegetation: a generally cooler and drier climate and a lower level of atmospheric CO<sub>2</sub>. In order to assess the relative impact of climate and atmospheric CO<sub>2</sub> changes on the global vegetation, we simulate the potential modern vegetation and the glacial vegetation with the dynamical global vegetation model ORCHIDEE, driven by outputs from the IPSL_CM4_v1 atmosphere-ocean general circulation model, under modern or glacial CO<sub>2</sub> levels for photosynthesis. ORCHIDEE correctly reproduces the broad features of the glacial vegetation. Our modelling results support the view that the physiological effect of glacial CO<sub>2</sub> is a key factor to explain vegetation changes during glacial times. In our simulations, the low atmospheric CO<sub>2</sub> is the only driver of the tropical forests regression, and explains half of the response of temperate and boreal forests to glacial conditions. Our study shows that the sensitivity to CO<sub>2</sub> changes depends on the background climate over a region, and also depends on the vegetation type, needleleaf trees being much more sensitive than broadleaf trees in our model. This difference of sensitivity leads to a dominance of broadleaf types in the remaining simulated forests, which is not supported by pollen data, but nonetheless suggests a potential impact of CO<sub>2</sub> on the glacial vegetation assemblages. It also modifies the competitivity between the trees and makes the amplitude of the response to CO<sub>2</sub> dependent on the initial vegetation state.