Recent geophysical work on the continental shelf of central and northern West Greenland has enabled the known onshore geology of the West Greenland Basin to be extended into the offshore region and the major graben running the length of the continental shelf in Melville Bugt to be defined in some detail. Two zones are observed within the offshore extension of the West Greenland Tertiary basalts. The eastern zone corresponds to dipping basalts at shallow depth similar to those occurring onshore on Hareøen, outermost Nûgssuaq, Ubekendt Ejland, and southwestern Svartenhuk. The more westerly zone corresponds to sub-horizontal to horizontal basalts whose top occurs at a depth of up to 1 km, the depth increasing towards the west and south. In the upper part of this offshore sequence the basalts are believed to be interlayered with Tertiary sediments. The Melville Bugt graben is shown to be a major continuous feature parallel to the coast of northwestern Greenland with sediment thicknesses of 7–10 km. The graben is believed to have been formed at the time of initial rifting of Canada and Greenland.