Wide-angle reflection/refraction seismic data were acquired on a 450-km-long transect in southern Baffin Bay extending from Baffin Island to Greenland. Dense air gun shots were recorded on 22 ocean bottom seismometers. A P wave velocity model was developed from forward and inverse modeling of the observed travel times. Beneath the Baffin Island shelf, a three-layered continental crust is observed with velocities of 5.5 to 6.9km/s. Typical for transform margins, there is a sharp transition between continental and oceanic crust. Off Baffin Island, 7-km-thick oceanic crust is interpreted to lie in a major transform fault identified on the gravity map. Beneath the deep Baffin Bay basin, 9-km-thick oceanic crust is encountered but thins to 6km within an assumed fracture zone. The thicker than normal oceanic crust indicates an ample magma supply, possibly related to melt extracted from a mantle plume. Seaward of the Greenland continental crust, 20-km-thick igneous crust (6.3 to 7.3km/s) is encountered in a 25-km-wide zone interpreted as a leaky transform fault that can be correlated southward through Davis Strait. The igneous crust is bounded by a 20-km wide basin to the west, underlain by 4-km-thick crust of unknown affinity. This structure is probably associated with transform movements. A high-velocity lower crustal layer (7.1km/s) of 8km thickness is indicated beneath the Greenland crust and can be correlated into the adjacent thick igneous crust. Both the thick igneous and Greenland crust are covered by up to 4km of Paleogene volcanics (5.2 to 5.7km/s).