The atmosphere–ocean general circulation models (AOGCMs) used for the IPCC 4th Assessment Report (IPCC AR4) are evaluated for the Greenland ice sheet (GrIS) current climate modelling. The most suited AOGCMs for Greenland climate simulation are then selected on the basis of comparison between the 1970–1999 outputs of the Climate of the twentieth Century experiment (20C3M) and reanalyses (ECMWF, NCEP/NCAR). This comparison indicates that the representation quality of surface parameters such as temperature and precipitation are highly correlated to the atmospheric circulation (500 hPa geopotential height) and its interannual variability (North Atlantic oscillation). The outputs of the three most suitable AOGCMs for present-day climate simulation are then used to assess the changes estimated by three IPCC greenhouse gas emissions scenarios (SRES) over the GrIS for the 2070–2099 period. Future atmospheric circulation changes are projected to dampen the zonal flow, enhance the meridional fluxes and therefore provide additional heat and moisture to the GrIS, increasing temperature over the whole ice sheet and precipitation over its northeastern area. We also show that the GrIS surface mass balance anomalies from the SRES A1B scenario amount to −300 km3/year with respect to the 1970–1999 period, leading to a global sea-level rise of 5 cm by the end of the 21st century. This work can help to select the boundaries conditions for AOGCMs-based downscaled future projections.