The Antarctic contribution to sea-level rise has long been uncertain. While regional variability in ice dynamics has been revealed, a picture of mass changes throughout the continental ice sheet is lacking. Here, we use satellite radar altimetry to measure the elevation change of 72% of the grounded ice sheet during the period 1992–2003. Depending on the density of the snow giving rise to the observed elevation fluctuations, the ice sheet mass trend falls in the range −5–+85Gtyr−1. We find that data from climate model reanalyses are not able to characterise the contemporary snowfall fluctuation with useful accuracy and our best estimate of the overall mass trend—growth of 27±29Gtyr−1—is based on an assessment of the expected snowfall variability. Mass gains from accumulating snow, particularly on the Antarctic Peninsula and within East Antarctica, exceed the ice dynamic mass loss from West Antarctica. The result exacerbates the difficulty of explaining twentieth century sea-level rise.