Projections of future global sea level depend on reliable estimates of changes in the size of polar ice sheets. Calculating this directly from global general circulation models (GCMs) is unreliable because the coarse resolution of 100km or more is unable to capture narrow ablation zones, and ice dynamics is not usually taken into account in GCMs. To overcome these problems we have coupled a high resolution (20km) dynamic ice sheet model to the Hadley Centre GCM, HadCM3. A novel feature is the use of two-way coupling, so that climate changes in the GCM drive ice mass changes in the ice sheet model which, in turn, can alter the future climate through changes in orography, surface albedo and fresh water input to the model ocean. At the start of our main experiment the atmospheric carbon dioxide concentration was increased to four times the pre-industrial level and held constant for 3000 years. By the end of this period the Greenland ice sheet is almost completely ablated and has made a direct contribution of approximately 7 m to global average sea-level, causing a peak rate of sea level rise of 5mm per year early in the simulation. We have examined the effect of ice sheet depletion on global and regional climate and found that apart from the sea level rise the long term effect on global climate is small. However, there are some significant regional climate changes which appear to have reduced the rate at which the ice sheet ablates.