ASA Târgu Mureș was founded in 1962 and in August 1964 merged with Mureşul Târgu Mureş, the descendant of Voinţa Târgu Mureş.
The club's best performance was a 2nd place in the Romanian First League, at the end of the 1974–75 season. It participated in 3 UEFA Cup campaigns, but was eliminated in the 1st round on all 3 occasions: in 1975–1976 by Dynamo Dresden, in 1976–1977 by Dinamo Zagreb and in 1977–1978 by AEK Athens. The team had a much better performance in the Balkans Cup in 1973 when it reached the final but lost against Lokomotiv Sofia.
Between 1962 and 1989 it played for 20 seasons in the Liga I and the rest in the Liga II. Between 1990 and 2002 it played for one season in the Liga I, in the 1991–92 season, and the rest in the Liga II. At the end of the 2001–02 season it relegated to the Liga III for the very first time in its history, and was dissolved soon after, in 2005.
The most famous player that wore the red-blue jersey was László Bölöni. He played 406 matches and scored 64 goals for ASA. He also won the European Champions Cup in 1986 with Steaua Bucharest. He coached the Romania national football team, France Ligue 1 teams Nancy, Rennes and AS Monaco and Portuguese club Sporting. He also was the coach of Standard Liège from July 2008 until February 2010. László Bölöni won the Belgian national title in 2009 after a thrilling play-off against great rival Anderlecht. He also won a title with Sporting CP in 2002, their last to date.
Another notable player was Florea Ispir. He played 485 matches in the Liga I, all for ASA, and scored 2 goals. He is ranked 3rd all-time among the players with most appearances in the Liga I.