We estimate the sea-ice extent and basal melt of Antarctic ice shelves at the Last Glacial Maximum (LGM) using a coupled ice-shelf-sea-ice-ocean model. The shape of Antarctic ice shelves, ocean conditions and atmospheric surface conditions at the LGM are different from those in the present day; these are derived from an ice-shelf-ice-sheet model, a sea-ice-ocean model and a climate model for glacial simulations, respectively. The winter sea ice in the LGM is shown to extend up to ∼7° of latitude further equatorward than in the present day. For the LGM summer, the model shows extensive sea-ice cover in the Atlantic sector and little sea ice in the other sectors. These modelled sea-ice features are consistent with those reconstructed from sea-floor sedimentary records. Total basal melt of Antarctic ice shelves in the LGM was ∼2147 Gt a–1, which is much larger than the present-day value. More warm waters originating from Circumpolar Deep Water could be easily transported into ice-shelf cavities during the LGM because the full glacial grounding line extended to shelf break regions and ice shelves overhung continental slopes. This increased transport of warm water masses underneath an ice shelf and into their basal cavities led to the high basal melt of ice shelves in the LGM.