Cleveland Robinson was born in 1914 in Swabys Hope, a rural parish of Jamaica. After serving as a local constable and an elementary school teacher, he emigrated to the United States in 1944. On arrival he took a job in a Manhattan dry goods store and very soon became active in District 65, Distributive Workers. After organizing his own shop in 1947, he went on to become a steward, and then a full-time organizer for the union. He was elected vice-president in 1950 and secretary-treasurer in 1952, a position he held until his retirement in 1992. During the period when District 65 was affiliated with the Retail, Wholesale and Department Store Workers Union (RWDSU), Robinson held the positions of international vice-president and executive board member of that union. After longstanding disagreements with the RWDSU about the pace of organizing in the South and efforts to reach minority workers, District 65 pulled out and organized the National Council of Distributive Workers of America; Cleveland Robinson was elected president of the new body. District 65 finally affiliated with the United Auto Workers (UAW) in 1981. At that time the union was comprised of 33,000 members, one half of whom were women, and one third minority workers; it had locals in 37 states, Canada and Puerto Rico.

A close associate of A. Philip Randolph, Robinson was founding member and vice-president of the Negro American Labor Council; he assumed the presidency of the 40,000-member NALC when Randolph retired in 1966. In 1971 he helped to found the Council of Black Trade Unionists, successor organization to the NALC, and served as its first vice president.

In addition to his union activity, Cleveland Robinson was a stalwart of the civil rights movement. He was administrative chairman and one of the key organizers of the August 1963 March on Washington for Jobs and Freedom. A friend and advisor on labor matters to Martin Luther King, Jr., he was an active member of the National Urban League and the NAACP, a director of the Southern Christian leadership Council, and a trustee of the Martin Luther King, Jr. Center in Atlanta, GA. He was also a leader in the struggle to mobilize American opposition to apartheid in South Africa and supported movements for labor and human rights in many African nations. He sat on the steering committee of the American Committee for Africa, and served as Commissioner of the New York City Commission for Human Rights during the administrations of Mayors Wagner and Lindsay. As co-chair of the committee that organized Nelson Mandela's visit to New York City in 1990, he spearheaded a massive fund-raising campaign among the city's trade unions to defray the expenses of the event. At the time of his death he was chair of the New York State Martin Luther King, Jr., Commission, which worked toward having King's birthday declared a legal holiday and sponsors observances of the day and educational programs focusing on civil rights throughout the state each year. He was the recipient of New York State's Martin Luther King, Jr. Medal of Freedom in 1987 and the Eugene V. Debs/Norman Thomas Award of the New York Democratic Socialists of America in 1984.

His first wife was Sue Eliza Robinson, a department store worker and member of District 65; and they had two sons and a daughter. After her death in 1976 he married again, Doreen McPherson Robinson. He suffered severely from glaucoma for many years, and was considered legally blind by 1970; but his level of commitment and activity was in no way impaired by this disability. He never lost touch with his Jamaican origins and traveled to the island often, keeping up a keen interest in a number of Jamaican-American political, cultural and fraternal organizations. Cleveland Robinson died of kidney failure in New York City in August 1995.