The Greenland Ice Sheet (GIS) is losing mass at a high rate(1). Given the short-term nature of the observational record, it is difficult to assess the historical importance of this mass-loss trend. Unlike records of greenhouse gas concentrations and global temperature, in which observations have been merged with palaeoclimate datasets, there are no comparably long records for rates of GIS mass change. Here we reveal unprecedented mass loss from the GIS this century, by placing contemporary and future rates of GIS mass loss within the context of the natural variability over the past 12,000 years. We force a high-resolution ice-sheet model with an ensemble of climate histories constrained by ice-core data(2). Our simulation domain covers southwestern Greenland, the mass change of which is dominated by surface mass balance. The results agree favourably with an independent chronology of the history of the GIS margin(3,4). The largest pre-industrial rates of mass loss (up to 6,000 billion tonnes per century) occurred in the early Holocene, and were similar to the contemporary (ad 2000-2018) rate of around 6,100 billion tonnes per century(5). Simulations of future mass loss from southwestern GIS, based on Representative Concentration Pathway (RCP) scenarios corresponding to low (RCP2.6) and high (RCP8.5) greenhouse gas concentration trajectories(6), predict mass loss of between 8,800 and 35,900 billion tonnes over the twenty-first century. These rates of GIS mass loss exceed the maximum rates over the past 12,000 years. Because rates of mass loss from the southwestern GIS scale linearly(5)with the GIS as a whole, our results indicate, with high confidence, that the rate of mass loss from the GIS will exceed Holocene rates this century.