Sumburgh Links was surveyed and the grass strips laid out by Captain E. E. Fresson of Highland Airways in 1936: the airport was opened on 3 June of that year with the inaugural flight from Aberdeen (Kintore) by the De Havilland Dragon Rapide G-ACPN piloted by Fresson himself. It was also one of the first airfields to have RDF facilities, due to the frequency of low cloud and fog and the proximity of Sumburgh Head. The runways were built at the instigation of Capt. Fresson, who had proved to the Navy at Hatston (Orkney) that runways were essential to maintain all-round landing facilities over the winter months. This was taken up by the RAF after the obvious success of the Hatston experiment.

The former RAF Sumburgh airfield had three runways, two of which, although extended, remain in use by the present airport. The longest was originally 800 yd (730 m), and the shorter ran for 600 yd (550 m) from shoreline to shoreline. No. 404 Squadron operated Beaufighter Mark VI and X aircraft from this station on coastal raids against Axis shipping off the coast of Norway and in the North Sea. The airport is unusual in that it has a 550 m (1,804 ft) helicopter runway as opposed to the usual helipad. The western end of runway 09/27 crosses the A970 road between Sumburgh (including the airport) and the rest of the island; access is controlled by a level crossing with barriers closed whenever a flight is taking off or landing.

Ownership of the company transferred from the UK Civil Aviation Authority to the Secretary of State for Scotland on 1 April 1995, and subsequently to the Scottish Ministers. HIAL receives subsidies from the Scottish Ministers in accordance with Section 34 of the Civil Aviation Act 1982 and is sponsored by Transport Scotland which is an Executive Agency of the Scottish Government and accountable to Scottish Ministers.