Jan Mrvík came from an athletic family, as his father played hockey (field) and his mother was a handball player. Jan chose rowing because of the nearby Slavoje Vyšehrad shipyard and he advanced to the Czechoslovak national team in the 1960s. In 1962 Mrvík competed at the World Championships and then helped Czechoslovakia win a bronze medal at the 1963 European Championships. The highlight of his career came in helping the Czechoslovak eight win bronze at the 1964 Tokyo Olympics.
Mrvík also competed at the 1966 World Championships in the eight, making the final but not the podium. He was a seven-time national champion and he had six wins in the traditional eight race for the Praha mayor’s shield. From 1967-76 Mrvík coached the women’s national team and then coached his club, Slavoj Vyšehrad. He also worked as an official in the Blesk rowing club.