Six Greenland sharks, Somniosus microcephalus (Bloch and Schneider, 1801), 190–355 cm fork length, were tracked under land-fast sea ice off northern Baffin Island (73.2°N; 85.3°W) between 16 and 28 May 1999, using ultrasonic telemetry. The sharks were tracked continuously for periods of 5.5–13.0 h, with the tracks of two individuals lasting 31.4 and 42.8 h, respectively, each with an interval when the track was lost. Several sharks dove after release and moved along the ocean bottom for the duration of the tracking period, while others varied their movements regarding course and depth. Two sharks made repeated visits to within 11 m of the ice–water interface from deeper water. The tracked sharks exhibited no apparent depth or temperature preferences, and pooled data indicated that sharks remained deep during the morning and gradually moved into shallower depths through the afternoon and night. Rates of descent (average=0.099 m s−1) were significantly greater than rates of ascent (average=0.058 m s−1) for all sharks, and the average rate of horizontal movement over ground was estimated as 0.215 m s−1. Based on the movements of tracked sharks and information contained in the literature, S. microcephalus may prey on seals in areas covered by land-fast sea ice.