We use 22 monthly GRACE (Gravity Recovery and Climate Experiment) gravity fields to estimate the linear trend in Greenland ice mass during 2002--2004. We recover a decrease in total ice mass of 82 ¿ 28 km3 of ice per year, consistent with estimates from other techniques. Our uncertainty estimate is dominated by the effects of GRACE measurement errors and errors in our post glacial rebound (PG) correction. The main advantages of GRACE are that it is sensitive to the entire ice sheet, and that it provides mass estimates with only minimal use of supporting physical assumptions or ancillary data.