Ödön Gróf started swimming competitively in the colors of the Pécs Athletic Club in 1930. He won his first youth Hungarian championship in 1931. At the senior level he won 15 individual and 10 relay gold medals in the Hungarian championship. In 1933, he was invited to join the national team preparing for the Berlin Olympics. From 1934, he competed as a swimmer of the UTE. At the European Championships in Magdeburg in 1934, he won a gold medal as a member of the 4x200 metres relay. At the College World Games in 1935 and 1937, he finished first four times along with one second place. At the 1936 Summer Olympic Games he was eliminated in the 100 metres freestyle during the preliminaries, and reached the semi-final in the 400 metres. With the 4x200 m relay, they broke the European record and finished third.
After his retirement in 1945, he became the head coach of the swimming department of UTE and later Újpesti Dózsa. After the 1956 revolution, he went abroad and settled in the United States.