The relationship between the Surface Mass Balance (SMB) of the Greenland Ice Sheet (GrIS) and the North Atlantic Oscillation (NAO) is examined from numerical simulations performed with a new atmospheric stretched grid configuration of the Centre National de Recherches Météorologiques – Coupled Model (CNRM-CM) version 5.2 under three periods : preindustrial climate, a warm phase (early Eemian, 130 ka BP) and a cool phase (glacial inception, 115 ka BP) of the last interglacial. The horizontal grid of the atmospheric component of CNRM-CM5.2 is stretched from the tilted pole on the Baffin Bay (72° N, 65° W) in order to obtain a higher spatial resolution on Greenland. The correlation between simulated SMB anomalies averaged over Greenland and the NAO index is weak in winter and significant in summer (about 0.6 for the three periods). In summer, spatial correlations between the NAO index and SMB display different patterns from one period to another. These differences are analysed in terms of the respective influence of the positive and negative phases of the NAO on accumulation and melting. Accumulation in South Greenland is significantly correlated with the positive (negative) phase of the NAO in a warm (cold) climate. Under preindustrial and 115 ka climates, melting along the margins is more correlated with the positive phase of the NAO than with its negative phase, whereas at 130 ka it is more correlated with the negative phase of the NAO in North and North-East Greenland.