We present a glacial isostatic adjustment (GIA) model for Antarctica. This is driven by a new deglaciation history that has been developed using a numerical ice-sheet model, and is constrained to fit observations of past ice extent. We test the sensitivity of the GIA model to uncertainties in the deglaciation history, and seek earth model parameters that minimize the misfit of model predictions to relative sea-level observations from Antarctica. We find that the relative sea-level predictions are fairly insensitive to changes in lithospheric thickness and lower mantle viscosity, but show high sensitivity to changes in upper mantle viscosity and constrain this value (95 per cent confidence) to lie in the range 0.8–2.0 × 1021 Pa s. Significant misfits at several sites may be due to errors in the deglaciation history, or unmodelled effects of lateral variations in Earth structure. When we compare our GIA model predictions with elastic-corrected GPS uplift rates we find that the predicted rates are biased high (weighted mean bias = 1.8 mm yr–1) and there is a weighted root-mean-square (WRMS) error of 2.9 mm yr–1. In particular, our model systematically over-predicts uplift rates in the Antarctica Peninsula, and we attempt to address this by adjusting the Late Holocene loading history in this region, within the bounds of uncertainty of the deglaciation model. Using this adjusted model the weighted mean bias improves from 1.8 to 1.2 mm yr–1, and the WRMS error is reduced to 2.3 mm yr–1, compared with 4.9 mm yr–1 for ICE-5G v1.2 and 5.0 mm yr–1 for IJ05. Finally, we place spatially variable error bars on our GIA uplift rate predictions, taking into account uncertainties in both the deglaciation history and modelled Earth viscosity structure. This work provides a new GIA correction for the GRACE data in Antarctica, thus permitting more accurate constraints to be placed on current ice-mass change.