Results from a 28-year simulation (1979?2006) over the Greenland ice sheet (GIS) reveal an increase of the solid precipitation (+0.4±2.5 km³ yr^?2) and the run-off (+7.9±3.3 km³ yr^?2) of surface melt water. The net effect of these competing factors leads to a significant Surface Mass Balance (SMB) loss rate of ?7.2±5.1 km³ yr^?2. The contribution of changes in the net water vapour fluxes (+0.02±0.09 km³ yr^?2) and rainfall (+0.2±0.2 km³ yr^?2) to the SMB variability is negligible. The melt water supply has increased because the GIS surface has been warming up +2.4°C since 1979. Latent heat flux, sensible heat flux and net solar radiation have not varied significantly over the last three decades. However, the simulated downward infra-red flux has increased by 9.3 W m^?2 since 1979. The natural climate variability (e.g. the North Atlantic Oscillation) does not explain these changes on the GIS. The recent global warming, due to the greenhouse gas concentration increase induced by the human activities, could be a cause of these changes. The doubling of the surface melt water flux into the ocean over the period 1979?2006 suggests that the overall ice sheet mass balance has been increasingly negative, given the probable meltwater-induced outlet glacier acceleration. This study suggests that an increased melting dominates over an increased accumulation in a warming scenario and that the GIS would likely continue to loose mass in the future. A GIS melting would have an effect on the stability of the thermohaline circulation (THC) and the global sea level rise.