Barber was born in Shreveport, Louisiana . He graduated from the University Of Arkansas in 1954, turned professional four years later, and won his first PGA Tour event in 1964. He notched up eleven tour wins in total, but did not win a Major Championship . He played on the Ryder Cup team in 1969 and 1971.
Barber became eligible to play on the Senior PGA Tour around a year after is was founded. He was one of the dominant players on the tour throughout the 1980s, competing on even terms with players who had had much more distinguished earlier careers such as Lee Trevino and Arnold Palmer . His twenty four wins on the Tour included five senior majors, three of them U.S. Senior Open s.