Rad was founded in 1958 by workers of the GRO Rad company. From the start the club had two major local rivals: Banjica and Jajinci, these rivalries were the rivals of the company but quickly it passed to football. The following individuals are considered as club's founders: Petar Đerasimović, the first president, Radojica Tanasijević, the first general selector, Željko Marjanović, the first financial adviser, and Ljubomir Lazić, the first vice president. The players that have played in 1958 can feel like founders as well, Rad had a lot of young players that were schooled in the First league teams, some players would include: Lazar Slavković, Đurđe Ivković, Vladimir Acević, Teodor Šušnjar, Milan Abramović, Brana Djaković, Aleksandar Banić, Živojin Rafailović, Aleksandar Andrejić, and a little later Sreten "Sele" Antić, Milan "Selja" Jovanović, and others.
The first head coach was Nikola Marjanović. The parliament has given the club a pitch in the center of Banjica, a few concrete stands were made, and later locker rooms were added, as well as the restaurant. The club had supporters in the Banjica region,which followed their club away and home. Rad quickly got promoted to the Belgrade League. In the period from 1965 to 1969, a change of generations had taken place. At that time the leaders were Ljubomir Lazić and Radomir Antić, notable managers were Đorđević and Đurđević, leaders for the players were Ratomir Janković, Vlada Vlaović, Matović, Zoran Bulatović, Dutina, Čeh and others.
The stadium of Rad is the King Petar I Stadium, commonly known as "Stadion na Banjici" (Stadium at Banjica), which is located in the southern part of Belgrad's Banjica neighbourhood, and holds about 6,000 people. It was built in 1977 although its stand dates back to the pre-WWII period when it was used for military parades and other state celebrations during the Kingdom of Yugoslavia.
The club official website considers Duško Ajder and Dragan Kokotović as club´s two major legends. Beside them, important players in different historical periods are considered Miodrag Vranješ, Ratomir Janković and Lazar Slavković.