Dr. George J. Kelley Jr., 57, who retired as an Air Force colonel in 1967 and later spent 19 months as Fairfax County executive before leaving that post in December 1972, died of cancer yesterday at Anne Arundel Hospital in Annapolis.

During Dr. Kelley's term as county executive, the county's bond rating improved from BAA to A, sewage treatment was expanded, and a computerized accounting system was introduced.

Under Virginia law, county executives hold office by appointment rather than election. It is their job to run the daily operations of the government and provide policy options for the elected county supervisors who then act on them.

Some Fairfax citizens criticized Dr. Kelley as being too strong an executive. But Reynold Thomas, the president of the Fairfax Federation of Citizens Associations in 1972, said that Dr. Kelley was "a modern manager . . . the guiding light to fiscal planning that you can follow and track."

Dr. Kelley's disagreements with members of the Board of Supervisors ranged from the personal to the philosophic. He abruptly resigned in February 1972 after a supervisor suggested that Dr. Kelley had withheld a sewage report from the board. Dr. Kelley was asked to reconsider his resignation and returned to his post.

The board also wanted to take steps to limit population growth, which had increased from 98,557 in 1950 to an estimated 520,000 in 1972. Dr. Kelley believed continued population growth would help the county by generating larger tax revenues while many of the county's costs would remain about the same.

Dr. Kelley's resignation came after he testified before Congress that other lternatives should be explored before Metro was allowed to take over area bus lines. The county board favored a bill before Congress approving the takeover and accepted Dr. Kelley's resignation.

Dr. Kelley had joined the county government as a deputy executive in June 1968. As a private management consultant he had directed a study that recommended sweeping changes in the government. He was hired to put the recommendations into effect and was promoted to county executive in March 1971.

Dr. Kelley was born in Annapolis. He was a graduate of the University of Virginia and earned master's and doctor's degrees in business administration at George Washington University.

He became an officer in the Army Air Corps during World War II, serving as a navigator in Europe. Postwar tours of duty include seven years at the Pentagon in the 1960s, including his final two years as a legislative liason officer in the office of the secretary of defense.

He held the Distinguished Flying Cross and the Legion of Merit with oak leaf cluster.

Dr. Kelley had been head of the management consulting division of Camp, Dresser & McKee, an environmental engineering firm, for the past three years.

He is survived by his wife, Elma K., and a daughter, Martha Kelley, both of the home in Annapolis; another daughter, Patricia Kelley, of Arlington; two sons, Michael G., of Springfield, and Rodney, of Harrisburg, Pa.; a brother, Edward W., of San Antonio, and one grandchild. CAPTION: Picture, DR. GEORGE J. KELLEY JR.