In 1974 a football called Mohemat Sazi was established in Tehran. The team never had any major success and only played in the lower leagues of the Iranian football league system. They came close to making it to Tehran's top football league in the 1980s. In the early 1990s the club was sponsored by a company named Maham. During the later stages of the club's history they were sponsored by Sanam, an electronics company.
In 2002 the club's shares were sold to Saba Battery Company (also known as Niru Company) which is under the control of Iran's Ministry of Defense. Due to the club's greatly improved financial status the team was able to purchase talented players and were promoted to the Iran Pro League in 2004.
The team debuted in the Iran Pro League in the 2004–05 season and made the headlines when they signed Iranian legend and FIFA all time greatest international goalscorer Ali Daei from Persepolis. With the help of Daei the team was able to secure a berth for the Asian Champions League after winning the 2005 Hazfi Cup, however failing to make it out of their group. In the same year Saba won the Iranian Super Cup defeating league champions Foolad 4–0. After the departure of Ali Daei in 2006, Saba signed former Bosnia and Herzegovina international Alen Avdić as his replacement. In 2007 Saba once again made the final of the Hazfi Cup, this time losing 4–0 to Sepahan on aggregate.
In 2008 Saba relocated to Qom because the city of Tehran had many football teams with low attendance figures. Saba was one of the few teams of the league in 2008–09 season which did not change managers during the season and finished in 6th position at the end of the season something that happened again in the next season. In the 2011–2012 Persian Gulf Cup, Saba Qom finished 4th securing a play–off spot for the 2013 AFC Champions League. In the play–off Saba lost to Al Shabab on penalties and failed to qualify to the group stage.