We use an ensemble of models participating in the Coupled Model Intercomparison Project phase 6 (CMIP6) to analyse the number of days with extreme winter precipitation over Northern Europe and its relationship to the North Atlantic Oscillation (NAO), for the historical period 1950-2014 and two future 21st-century scenarios. Here we find that over Northern Europe, the models project twice more extreme precipitation days by the end of the 21st century under the high-emission scenario compared to the historical period. We also find a weakening of the NAO variability in the second half of the 21st century in the high greenhouse gas emission scenario compared to the historical period, as well as an increasing correlation between extreme winter precipitation events and the NAO index in both future scenarios. Models with a projected decrease in the NAO variability across the 21st century show a positive trend in the number of days with extreme winter precipitation over Northern Europe. These results highlight the role played by NAO in modulating extreme winter precipitation events.