The analysis of seafloor glacial landforms can provide important constraints on the past behaviour of ice sheets, including their extent at the Last Glacial Maximum and the controls on their subsequent retreat. The continental shelf and slope offshore of northwest Greenland have been sparsely surveyed, however, limiting our understanding of ice sheet extent and dynamics in this sector during the pre-satellite era. Here we use newly acquired high-resolution geophysical data to map and interpret the distribution of glacial landforms across the hitherto unexplored banks of northern Melville Bay and the adjacent slope and deep-sea basin. In contrast to previous conceptual models, our seafloor observations suggest that shelf-break glaciation was attained along the entire northwest Greenland margin at the Last Glacial Maximum, including beyond the shallow banks. The landforms that we map on the continental slope provide strong support for the existence of an ice shelf spanning northern Baffin Bay. Sub-ice shelf keel scours in water depths of down to 1220 m reveal that this ice shelf was at least 1100 m thick at its grounding zone. The orientation of sub-ice shelf landforms suggests that the ice shelf was fed mainly by the supply of ice to northern Baffin Bay from the Lancaster Sound Ice Stream of the Canadian Arctic Archipelago. The Baffin Bay ice shelf buttressed several large ice streams of the Greenland, Innuitian and Laurentide ice sheets at the Last Glacial Maximum, and its break-up may have contributed to instigating the deglacial retreat of these ice streams from the shelf edge.