The airline was established and started operations in 1990. It was founded as NAWA Air Transport, the first privately owned airline in Hungary after World War II. In 1993 it was acquired by Farner Air Transport and was renamed Farner Air Transport Hungary. It became Farnair Hungary in 1997. It is wholly owned by Farnair Switzerland.
On 4 June 2015, ASL Aviation Group, the parent company of Farnair Hungary, announced that Farnair Hungary will be rebranded as ASL Airlines Hungary.
On 27 January 2005, a Farnair Hungary Let L-410 aircraft was carrying out a non-directional beacon let-down with radar assistance at Iași Airport, Romania, but when the crew notified air traffic control of their position over the airport beacon and their intention to turn right outbound, they were seen to turn left. Then the aircraft spiralled down to crash on the airfield. The two crew members on board were killed. There was light snow at the time.
On 5 August 2016, an ASL Airlines Hungary Boeing 737-476(SF), registered as HA-FAX, overshot runway 28 when landing at Il Caravaggio International Airport in Bergamo and came to a stop on the highway, 300 metres from the runway end. There were no injuries, but some cars were destroyed and the plane sustained substantial damage as a result of the incident.