Over recent decades, Greenland ice sheet surface melt has shown an increase both in intensity and spatial extent. Part of this water probably reaches the bed and can enhance glacier speed, advecting a larger volume of ice into the ablation area. In the context of a warming climate, this mechanism could contribute to the future rate of thinning and retreat of land-terminating glaciers of Greenland. These changes in ice flow conditions will in turn influence surface crevassing and thus the ability of water to reach the bed at higher elevations. Here, using a coupled basal hydrology and prognostic ice flow model, the evolution of a Greenland-type glacier subject to increasing surface melt is studied over a few decades. For different scenarios of surface melt increase over the next decades, the evolution of crevassed areas and the ability of water to reach the bed is inferred. Our results indicate that the currently observed crevasse distribution is likely to extend further upstream which will allow water to reach the bed at higher elevations. This will lead to an increase in ice flux into the ablation area which, in turn, accelerates the mass loss of land-terminating glaciers.