Moran was the son of Lewis Moran and Judy Moran. Mark Moran was his half-brother. Moran attended Penleigh and Essendon Grammar School. He met his future wife, Trisha Kane, at 15 years of age. She is the daughter of Les Kane, a Melbourne Painter and Docker and reputed criminal who was murdered in his family home on 19 October 1978.
During the 1990s Moran emerged as one of Melbourne's main dealers in party drugs. During this time he had a team of up and coming western suburbs gangsters led by Bluey Watkins and Toofie Abudul running drugs for him.
Moran was reported to have shot Carl Williams in the stomach during an argument in Gladstone Park on 13 October 1999, giving rise to lengthy violent turf wars known as the Melbourne gangland killings. Jason Moran had attended the funeral of another slain mobster, Victor Peirce.
Alphonse Gangitano and Moran, along with associate Mark John McNamara, were charged over an attack in the Sports Bar nightclub in King Street, Melbourne, on 19 December 1995, for which Moran received a term of imprisonment.
Moran was considered by many to be a "dead man walking" and when paroled from prison in September 2001 was allowed to leave Australia due to fears for his life. He later returned to give evidence in the inquest into the death of Gangitano on 20 November which began on 14 January 2002. Moran was suspected in Gangitano's murder.Gangitano was found dead in the laundry of his Templestowe house by his wife in 1998. A coroner found that Jason Moran and Graham Kinniburgh were present during Gangitano's murder in January 1998.
re-enactment scene of Jasons murder on the series "Underbelly" (no audio)
