The Greenland ice sheet has experienced increasing mass loss since the 1990s^,. The enhanced freshwater flux due to both surface melt and outlet glacier discharge is assuming an increasingly important role in the changing freshwater budget of the subarctic Atlantic. The sustained and increasing freshwater fluxes from Greenland to the surface ocean could lead to a suppression of deep winter convection in the Labrador Sea, with potential ramifications for the strength of the Atlantic meridional overturning circulation^,,. Here we assess the impact of the increases in the freshwater fluxes, reconstructed with full spatial resolution, using a global ocean circulation model with a grid spacing fine enough to capture the small-scale, eddying transport processes in the subpolar North Atlantic. Our simulations suggest that the invasion of meltwater from the West Greenland shelf has initiated a gradual freshening trend at the surface of the Labrador Sea. Although the freshening is still smaller than the variability associated with the episodic ‘great salinity anomalies’, the accumulation of meltwater may become large enough to progressively dampen the deep winter convection in the coming years. We conclude that the freshwater anomaly has not yet had a significant impact on the Atlantic meridional overturning circulation.