As a result of climate warming, glacial meltwater discharge has been increasing in Greenland. During the summers of 2015 and 2016, there were rapid increases in discharge from Qaanaaq Glacier in northwestern Greenland. These discharges resulted in floods that destroyed the road linking the settlement of Qaanaaq to Qaanaaq Airport. Field measurements were performed and a numerical model of glacier runoff was developed to quantify these discharges. The high discharge associated with the 2015 flood, estimated at 9.1 m3 s−1 (hourly mean), resulted from intensive glacier melting due to warm air temperature and strong winds, while the high discharge associated with the 2016 flood resulted from heavy rainfall (90 mm d−1) that led to a peak discharge estimated at 19.9 m3 s−1. The developed model, when used to investigate future glacier runoff under warming conditions, revealed a nonlinear increase in glacial melt with increasing temperature. Additionally, the model forecasted a threefold increase in total summer discharge, owing to a 4 °C rise in temperature. Thus, this study quantified the impact of a changing climate on glacier runoff, which gives insight into future risks of flood hazards along the coast of Greenland.