The Arctic climate is changing rapidly1. From 1979 to 2006, September sea-ice extent decreased by almost 25% or about 100,000 km2 per year (ref. 2). In September 2007, Arctic sea-ice extent reached its lowest level since satellite observations began3and in September 2008, sea-ice cover was still low. This development has raised concerns that the Arctic Ocean could be ice-free in late summer in only a few decades, with important economic and geopolitical implications. Unfortunately, most current climate models underestimate significantly the observed trend in Arctic sea-ice decline4, leading to doubts regarding their projections for the timing of ice-free conditions. Here we analyse the simulated trends in past sea-ice cover in 18 state-of-art-climate models and find a direct relationship between the simulated evolution of September sea-ice cover over the twenty-first century and the magnitude of past trends in sea-ice cover. Using this relationship together with observed trends, we project the evolution of September sea-ice cover over the twenty-first century. We find that under a scenario with medium future greenhouse-gas emissions, the Arctic Ocean will probably be ice-free in September before the end of the twenty-first century.