Nelson was born Haakon Robert Nielsen in San Francisco, California, the son of Norwegian immigrants, Betsy (née Christophersen) and Trygve Nielsen His year of birth has been subject to some debate, but his 1943 Army enlistment record and his 1993 voter registration records lists 1917 as the year of his birth. He began acting in school at the age of fifteen. He graduated from the University of California, Berkeley in 1941 and, because of his theatrical efforts in school, was almost immediately signed to a motion picture contract by Metro-Goldwyn-Mayer Studios.
As an MGM contract player, Nelson made his screen debut in the role as Paul Clark in Shadow of the Thin Man (1941) starring William Powell and Myrna Loy, with Donna Reed. He followed that with his role as Lew Rankin in the film noir crime/drama Johnny Eager (1942) starring Robert Taylor and Lana Turner. He played the lead in an MGM second feature war film A Yank on the Burma Road. (1942)
During his service in the United States Army in World War II, Nelson debuted on the Broadway stage in one of the leading roles, Bobby Grills, in Moss Hart's play Winged Victory (1943). His next Broadway appearance was as Peter Sloan in Hart's Light Up the Sky (1948), which was a first-rate success. He went on to appear on Broadway with Barbara Bel Geddes in the original Broadway production of The Moon is Blue; he was the last surviving original cast member of the production. During the play's run he also starred in a CBS half-hour drama called The Hunter, premiering in July 1952. He played Bart Adams, a wealthy young American whose business activities involved him in a series of adventures. He also appeared opposite Lauren Bacall in the Abe Burrows comedy Cactus Flower in 1965 and with Dorothy Loudon in The Fig Leaves Are Falling in 1969. Another Broadway role, that of Gus Hammer in The Rat Race (1949), kept Nelson away from the movies again, but after it closed he starred in the dual roles as Chick Graham and Bert Rand in The Man with My Face (1951), which was produced by Ed Gardner of radio fame.
He was the first actor to play James Bond on screen, in a 1954 adaptation of Ian Fleming's novel Casino Royale on the television anthology series Climax! (preceding Sean Connery's interpretation in Dr. No by eight years). Reportedly this was considered a pilot for a possible James Bond television series, though it is not known if Nelson intended to continue playing the character. Nelson played James Bond as an American agent whom some in the program call "Jimmy". In 2004, Nelson said, "At that time, no one had ever heard of James Bond ... I was scratching my head wondering how to play it. I hadn't read the book or anything like that because it wasn't well-known." Bond did not become well known in the U.S. until President John F. Kennedy listed From Russia, with Love among his ten favorite books in a 17 March 1961 Life Magazine article.
The program also featured Peter Lorre as the primary villain, Le Chiffre; Nelson later noted the opportunity to work with Lorre was the reason he took the role. Originally broadcast live, the production was believed lost until a kinescope emerged in the 1980s. It was subsequently released to home video, and is currently available on DVD as a bonus feature with the 1967 film adaptation of the novel.
Nelson played the lead in a 20-episode Western television series set in Canada and entitled Hudson's Bay, which featured George Tobias as his sidekick.
Nelson appeared as Grant Decker in "Threat of Evil", a 1960 episode of CBS's anthology series The DuPont Show with June Allyson. His additional television credits include guest appearances on Alfred Hitchcock Presents, Ben Casey, The Twilight Zone (episode "Stopover In A Quiet Town"), Dr. Kildare, and later years played a hobo on an episode of The Ropers . He appeared regularly on television in the 1960s, having been one of the What's My Line? mystery guests and later serving as a guest panelist on that popular CBS quiz show. Nelson appeared in both the stage and screen versions of Mary, Mary.
In 1978, he was nominated for a Tony Award for Best Actor in a Musical for his role as Dan Connors in the Broadway musical The Act (1977) with Liza Minnelli. His final appearance on Broadway was as Julian Marsh in 42nd Street (1986). William Goldman, in his 1968 book The Season, called Nelson a consummately professional actor.
"He was a very naturalistic, believable actor," said his agent, Francis Delduca. "He was good at both comedy and the serious stuff."
Among his other film credits were Airport and The Shining (as the hotel manager who interviews Jack Nicholson for a job opening), and he also appeared on such television series as Murder, She Wrote, Dallas, Cannon and Magnum, P.I. More recently, Nelson and his second wife spent a lot of time travelling. He planned to write a couple of books about his time on stage and in Hollywood.
From 1963 to 1966, he hosted portions of the NBC Radio program Monitor.
Nelson had two wives, actress Teresa Celli, married in 1951 and later divorced, and Nansilee ("Nansi") Hoy, to whom he was married until his death. Nelson and his second wife divided their time between homes in New York and France.
Barry Nelson died on April 7, 2007, while traveling in Bucks County, Pennsylvania, nine days before his 90th birthday. The cause of his death was unknown.