Grumman's engineers felt that the AA-5 design had more speed potential than the original Traveler, even with its 1975 improvements, and so embarked on an aerodynamic cleanup and redesign. Changes were made to the engine cowling and baffling to reduce cooling drag, the exhaust system was redesigned, the main landing gear fairings were further improved, the ventral fin was eliminated, and the horizontal tail was enlarged to allow a larger center of gravity range. Fuel capacity was increased from the Traveler's 37 US gallons to 52 gallons, thus increasing its range.

The new variant was named the AA-5A Cheetah and was introduced as a 1976 model in late 1975. In keeping with its namesake it was six knots (seven mph) faster than the Traveler with the same 150 hp (110 kW) Lycoming O-320-E2G powerplant. Because the Cheetah looked very much like the Traveler externally, Grumman's marketing department created a "leaping cheetah" emblem to differentiate it from the earlier AA-5.

Grumman sold its light aircraft division to Gulfstream Aerospace in 1978 and the division was renamed Gulfstream American. Gulfstream continued production of the AA-5A until 1979. A total of 900 Cheetahs were produced.