Nielsen grew up in Hellerup as the son of a well-off family who promoted his tennis talent and provided him with the German tennis trainer Kurt Pohmann. In 1947 he won the individual title of the junior tournament at Wimbledon by beating Sven Davidson in the final , the following year he won the junior title of the French Open . In 1953 he reached the final of Wimbledon, in which he was defeated by Vic Seixas, among other things by defeating the top seeded Ken Rosewall . In 1955 he reached the final of Wimbledon again, this time he lost to Tony Trabert . In mixed , he won the title at the US Open alongside Althea Gibson in 1957 , and together they both stood in the mixed final of Wimbledon the following year. In the course of his career between 1949 and 1960 he was able to win 49 international and 50 national Danish titles.
He was nominated for the Danish Davis Cup team for the first time in 1948 and met Egypt in his first encounter . He won his two singles, while the double encounter was lost. By 1960 he appeared in 65 singles and 31 doubles games for Denmark. He met the German Davis Cup team twice . In 1951 he lost to Gottfried von Cramm and Ernst Buchholz ; the following year he won against Buchholz and Horst Hermann .
After the end of his active career, Nielsen worked as a tennis trainer and referee, including at Grand Slam tournaments. Until the end of 2006 he worked as a commentator at Eurosport .
He was the grandfather of Frederik Nielsen , who also took up the professional career in tennis.