Floyd Freeman Graham was born in Roanoke, Texas on October 15, 1902. His family moved to nearby Denton when he was two years old so that he and his elder brother, Wynne, could attend school. Both brothers later attended North Texas State Normal College, and Wynne was among the first five students awarded bachelor's degrees in 1919. Floyd Graham graduated from Denton High School in 1919. During the 1920s, he appeared in ensembles on Fort Worth and Dallas radio, taught violin, and briefly served as band director at Denton High School.
The 1927-1928 edition of The Yucca, North Texas' yearbook at the time, devotes a page to the success of the Teachers College Band under Graham's direction, noting that "Teachers College has had a band for several years, but this year's group of musicians, under the direction of Floyd Graham, has been the most successful ever organized." The facing page in the yearbook further remarks that "Much of the success of both the band and orchestra is due to the untiring efforts of Floyd Graham," noting that Graham "received part of his education in the Teachers College. He has spent considerable time studying in Chicago."
Graham earned Teachers Certificate from Chicago Musical College in 1927 and a Bachelor of Music degree in violin there in 1931, later earning a Master of Music degree from the American Conservatory of Music in 1936. While in Chicago, Graham studied with Leo Sowerby, among others, and studied at Juilliard in the summer of 1939 with Ferde Grofé and Fritz Mahler.
At North Texas, Graham became best known for the stage band known as the Aces of Collegeland, which anchored the Saturday Night Stage Show in Denton. This weekly function helped launch the careers of numerous performers, including Pat Boone, Joan Blondell, Louise Tobin, Ann Sheridan, and the Moon Maids. The Aces of Collegeland also served as a forerunner of UNT's jazz studies program -- the first four-year accredited degree in the United States -- and its flagship One O'Clock Lab Band, as early jazz coursework at North Texas grew out of a demand for training in arranging for jazz and dance bands. Major instrumentalists who performed with the Aces include guitarist Herb Ellis, saxophonist and clarinetist Jimmy Giuffre, and bassist and cellist Harry Babasin.
Graham was also a member of the first Boy Scout troop organized in Denton, a longtime member of the Kiwanis Club, and served as a volunteer firefighter and fire chief, for which he received the Friend of Denton Award in 1969. In 1958, the student government established the 'Fessor Graham award, an annual award for outstanding teaching, and Graham was named the first emeritus professor at North Texas upon his retirement in 1973.
Floyd Graham died in Denton on August 18, 1974.