Granger was born Newport News, Virginia, one of six sons. His mother was a teacher and his father was a doctor from Barbados. He grew up in Newark, New Jersey and graduated from Dartmouth College in 1918.
In 1922, Granger was an extension worker with the New Jersey state vocational school for African American youth in Bordentown, New Jersey.
In 1930, he organized the Los Angeles chapter of the NUL. In 1934, he led the organization's efforts to promote trade unionism among African American workers and challenge racism by employers and labor organizations.
In 1940, Granger became the NUL’s assistant executive secretary in charge of industrial relations, and continued to work to integrate racist trade unions. In 1941, he led the NUL's effort to support the March on Washington proposed by A. Phillip Randolph, Bayard Rustin and A. J. Muste to protest racial discrimination in defense work and the Armed Forces. In 1945, he began working with the Department of Defense to desegregate the military, seeing first success with the Navy in February 1946. During the civil rights movement of the 1960s, he insisted that the NUL continue its strategy of "education and persuasion," a view which the NUL continued to support.
He remained a leading figure in social work over the years, and in 1952, served as president of the National Conference of Social Work.
Granger was a member of Alpha Phi Alpha fraternity.
Granger died in Alexandria, Louisiana in January 1976.
- Streator, George. "SCHOOL IN JERSEY AIDS NEGRO YOUTHS; Bordentown 'Exposes' Them to Trades and Skills While Promoting Self-Respect", The New York Times, November 21, 1948. Accessed June 3, 2010.
- CENTER OF MILITARY HISTORY, Washington DC. Morris J. MacGregor, Jr. 1985. INTEGRATION OF THE ARMED FORCES 1940-1965. World War II: The Navy. A Segregated Navy.