The exoplanet Gl581d (discovered in 2007) is relatively low mass and near to the outer edge of its system's habitable zone, which has led to much speculation on its possible climate. To help understand the possible conditions on this planet, we have developed a new universal 3D global climate model (GCM). It is derived from the LMD GCMs already used to simulate the Earth, Mars and other terrestrial atmospheres in the solar system, and hence has already been validated over a wide range of physical conditions. We have performed a range of simulations to assess whether, given simple combinations of chemically stable gases (CO2, H2O and N2), Gl581d could sustain liquid water on its surface. Compared to a Sun-like star, the red dwarf Gliese 581 allows higher planetary temperatures, because Rayleigh scattering is reduced. Taking into account the scattering greenhouse effect of both CO2 and H2O clouds, we find that several tens of bars of CO2 are sufficient to maintain global mean temperatures above the melting point of water. As Gl581d is probably in a tidally resonant orbit, condensables such as water and CO2 may be trapped on its dark sides or poles. However, we find that even with conservative assumptions, redistribution of heat by the atmosphere is enough to allow stable conditions with surface liquid water. A dense atmosphere of this kind is quite possible for such a large planet, and could be distinguished from other cases using future observations.Read less <