Robert Lawrence Stearns, a former president of the University of Colorado who was the father-in-law of Supreme Court Justice Byron White died Wednesday at his home in Denver after a long illness. He was 84.

Mr. Stearns was born in Halifax, Nova Scotia, and reared in Denver. He graduated from the University of Colorado in 1914, and received a law degree from Columbia University in 1916.

Mr. Stearns was president of the University of Colorado between 1935 and 1953. He took a leave of absence from 1943 to 1945 to serve a chief of the operations analysis division of the 13th and 20th Air Forces.

Mr. Stearns helped in the establishment of the Air Force Academy and in the passage in Colorado of legislation calling for nonpartisan selection of judges.

Mr. Stearns received the Medal of Freedom, a Salvation Army Award, the Regis College Civis Princeps Award, and a brotherhood award of the National Conference of Christians and Jews.

He was a member of Beta Theta Phi, Phi Delta Phi, and served as president of the Denver Bar Association in 1927, the Colorado Bar Association in 1936, and the Rotary Club of Denver in 1956. He was also a chairman of the American Council on Education.

At the time of his death, he was counsel for the Davis, Graham, and Stubbs law firm of Denver.

Mr. Stearns is survived by his wife, Amy; four daughters, Marion White of McLean, Amy Goodell of Berkeley, Calif., Judity Caughey of Denver, and Barbara Wooten of Englewood, Colo., a sister, Harriett Stewart of Wheatridge, Colo., and eight grandchildren.