Grumman Aerospace Corporation began design in the mid-1950s of a twin-turboprop executive transport which was intended for a crew of two and 10-14 passengers in typical corporate versions: an alternative high-density layout could seat a maximum of 24 passengers. Designated Grumman G-159 Gulfstream I, this was a conventional low-wing monoplane with pressurised accommodation, retractable tricycle landing gear, and powered by two Rolls-Royce Dart turboprops. The prototype was flown for the first time on 14 August 1958.

In addition to the production of civil Gulfstream Is, Grumman also supplied nine TC-4C aircraft to the US Navy. Required for the training of crews to serve with Grumman A-6A Intruder squadrons, they are easily distinguished from standard Gulfstreams by having a bulbous nose radome. Two other Gulfstream Is were acquired by the US Coast Guard under the designation VC-4A, these being used as VIP transports.

Most of the 200 Gulfstream Is that were built went to customers in North America, but a number of these are now being converted to Gulfstream I-C configuration. This programme was initiated by Gulfstream American Corporation (now Gulfstream Aerospace Corporation) following the acquisition of Grumman's Gulfstream division. The conversion entails a fuselage 'stretch' of 3.25m to provide seating for a maximum 37 passengers, but is otherwise little different from the original Gulfstream I.