The 1963–64 season was FC Dinamo București's 15th season in Divizia A. Dinamo realizes the first double in history. In addition to authoritarian rule in the championship, which they won for the third consecutive time, Dinamo wins the Romanian Cup, after beating Steaua Bucharest in the final. In the European Cup, Dinamo meets the multiple champions Real Madrid.
Before the season, Dinamo bought Emil Petru and Octavian Popescu, both from Stiinta Cluj, and Ion Haidu from Steagu Rosu Braşov. Florin Halagian was transferred to Petrolul Ploiesti and Nicolae Selymes to Steagu Rosu. Mircea Lucescu has been promoted from the youth team.