The northern Antarctic Peninsula is currently undergoing rapid atmospheric warming1. Increased glacier-surface melt during the twentieth century2, 3 has contributed to ice-shelf collapse and the widespread acceleration4, thinning and recession5 of glaciers. Therefore, glaciers peripheral to the Antarctic Ice Sheet currently make a large contribution to eustatic sea-level rise6, 7, but future melting may be offset by increased precipitation8. Here we assess glacier–climate relationships both during the past and into the future, using ice-core and geological data and glacier and climate numerical model simulations. Focusing on Glacier IJR45 on James Ross Island, northeast Antarctic Peninsula, our modelling experiments show that this representative glacier is most sensitive to temperature change, not precipitation change. We determine that its most recent expansion occurred during the late Holocene ‘Little Ice Age’ and not during the warmer mid-Holocene, as previously proposed9. Simulations using a range of future Intergovernmental Panel on Climate Change climate scenarios indicate that future increases in precipitation are unlikely to offset atmospheric-warming-induced melt of peripheral Antarctic Peninsula glaciers