Vollmer was the No.1 ranked German player in 1952 and 1955.Between 1953 and 1959 she competed in seven consecutive editions of the Wimbledon Championships and achieved her best singles result in 1953 when she reached the quarterfinal in which she lost in two sets to first-seeded and eventual champion Maureen Connolly.In 1947 she married doctor Johannes Vollmer.
In 1956 she received the Silbernes Lorbeerblatt (Silver Laurel Leaf), the highest sports award in Germany.