Future projections and past reconstructions of Antarctic Ice Sheet stability and sea-level rise depend on knowledge of continental shelf bathymetry, which controls water circulation under floating ice and interactions between the ice shelf and seafloor. We present a bathymetry model of the Venable Ice Shelf in the Bellingshausen Sea sector, from an inversion of airborne gravity data. The new model reveals troughs up to ~1.6 km deeper than previously mapped, providing pathways for warm Circumpolar Deep Water to access the grounding line. A bathymetric high beneath the western Venable Ice Shelf is identified as a former pinning point that has been intermittently grounded since ~1935 and allows us to interpret crevasse patterns in satellite imagery as evidence of mid-20th century ice-shelf thinning, extending the ice-shelf thickness record beyond the satellite era.