It is important to understand recent changes in the velocity of Greenland glaciers because the mass balance of the Greenland Ice Sheet is partly determined by the flow rates of these outlets. Jakobshavn Isbrae is Greenland's largest outlet glacier, draining about 6.5 per cent of the ice-sheet area, and it has been surveyed repeatedly since 1991 (ref. 2). Here we use remote sensing data to measure the velocity of Jakobshavn Isbrae between 1992 and 2003. We detect large variability of the velocity over time, including a slowing down from 6,700 m yr(-1) in 1985 to 5,700 m yr(-1) in 1992, and a subsequent speeding up to 9,400 m yr(-1) by 2000 and 12,600 m yr(-1) in 2003. These changes are consistent with earlier evidence for thickening of the glacier in the early 1990s and rapid thinning thereafter. Our observations indicate that fast-flowing glaciers can significantly alter ice discharge at sub-decadal timescales, with at least a potential to respond rapidly to a changing climate.