Robert Leroy Cochran was born in Avoca, Nebraska. He served in World War I, then ran for governor of Nebraska and won in 1934, defeating the Republican candidate, Dwight Griswold, by 17,388 votes (50,8% to 47.7%). He was re-elected in 1936, again defeating Griswold, this time by 55.9% to 43.1%. In 1938 he was elected for a third term as Governor, defeating the Republican candidate, Charles J. Warner, by 44% to 40.6%; a third candidate, Charles W. Bryan, received 15.4% of the vote. In 1940 he ran unsuccessfully for Nebraska senator, losing to Hugh Butler by 57% to 41.5%.
He served as a colonel in the U.S. Army during World War II.