Born in Okemah, Oklahoma, Barrow received a Bachelor of Arts degree from the University of Oklahoma in 1937 and a Bachelor of Laws from Southeastern State College (now Southeastern Oklahoma State University) in 1942.

He was in the United States Army during World War II from 1942 to 1946, and achieved the rank of major.

He was assistant chief counsel and acting chief counsel of the Southwestern Power Administration of the United States Department of the Interior in Tulsa from 1951 to 1954, then returned to private practice of law in Tulsa until 1962.

[1] On July 18, 1962, Barrow was nominated by President John F. Kennedy to a seat on the United States District Court for the Northern District of Oklahoma vacated by Judge Royce H. Savage.

[1] Barrow served as Chief Judge from 1962 until his death on February 26, 1979.