The 650 m long proglacial bedrock borehole DH-GAP04 is angled under the Greenland Ice Sheet and is the only bedrock borehole in the Arctic providing deep groundwater information at an active ice sheet setting. DH-GAP04 is drilled at the Greenland ice sheet margin and the lower part of the borehole extends in under the ice sheet. Permafrost is observed in the upper ~400 m of the borehole. DH-GAP04 is outfitted with a downhole instrument cluster that includes two inflatable packers, which divides the borehole in three sections: Section Up (400-561 m), Section Mid (561-571 m) and Section Low ( 571-651 m). Absolute pressure is measured in each section at 1-4 hour intervals and converted to hydraulic head. This dataset presents the daily average hydraulic head record spanning July, 2011 to December, 2018. Details on how absolute pressure is converted to hydraulic head is found in the accompanying "READ ME" file.