The first football club in Radanovići, which existed only few seasons, was founded in 1970. After many years, the club was refounded in June 1995 and in their first season the team gained promotion to the
Montenegrin Republic League for the 1996–97 season (third tier of the
FR Yugoslavia football system). After only three seasons in the Republic League, in the summer of 1999, OFK Grbalj (
OFC Humpback) became a member of the
FR Yugoslavia Second League, which was the biggest success of the team until 2006. OFK Grbalj spent four seasons in the Second Yugoslav League. After
Montenegrin independence, OFK Grbalj became a member of the
Montenegrin First League. In the 2006–07 season, the team achieved third place, just behind two of the most successful teams in national competitions,
Zeta and
Budućnost Podgorica. Over the next two seasons, OFK Grbalj finished as a fourth-placed team. During subsequent seasons, the team didn't achieve the same successes as in their first seasons in top-tier competition, but they were never relegated from the First League. OFK Grbalj holds two all-time records in the Montenegrin First League. On 29 May 2010 they defeated
Kom 11–0, which is the biggest margin of victory in the history of league. Five years later, on 23 May 2015, OFK Grbalj beat
Mornar in
Bar 7–0, which is the biggest away victory in league. In the 2016–17 season, OFK Grbalj had the greatest success in their history by reaching the
Montenegrin Cup final. They lost game against
Sutjeska 1–0. After 14 consecutive seasons in top-tier, OFK Grbalj finished as a last-placed team in
2019-20 Montenegrin First League. After the campaign full of disappointing results, team from Radanovići was relegated to
Montenegrin Second League.
First League Record For the first time, OFK Grbalj played in Montenegrin First League on season
2006–07. Below is a list of OFK Grbalj scores in First League by every single season.
OFK Grbalj in European competitions For the first time, OFK Grbalj played in European competitions on season
2007-08. They were first team from Montenegrin coastal region which played in
UEFA competitions. Until now, OFK Grbalj played two seasons in European cups. ==Honours==