Born in Vincennes, Indiana, he graduated from DePauw University in 1939, where he was a member of Phi Kappa Psi Fraternity, and earned a master's degree in economics from Harvard University in 1941.

He served in the United States Navy from 1942 to 1945, during World War II, with subchaser duty in the Mediterranean Sea and Atlantic Ocean. He received a Bronze Star for sinking a submarine off Anzio Beach.

After Barr returned from the war he engaged in the operation of grain elevators, theaters, real estate and publishing businesses. He was elected as a Democrat to the 86th United States Congress (1959-1961). He lost the 1960 election was appointed assistant for congressional relations to the U.S. Secretary of the Treasury and then in 1963 was appointed Chairman of the Federal Deposit Insurance Corporation.

He was Undersecretary of the Treasury from 1965 to 1968 during the administration of President Lyndon Johnson, and U.S. Secretary of the Treasury from December 21, 1968, to January 20, 1969, the shortest term of any Treasury Secretary. Because of this, US currency bearing his signature is said by some to be rare and hard to find. This is, for the most part, false.

Barr was president and chairman of American Security and Trust Company from 1969 to 1974 and chairman of Federal Home Loan Bank of Atlanta from 1977 to 1981. He died in 1996 in Playa del Carmen, Mexico.

This article incorporates facts obtained from the public domain Biographical Directory of the United States Congress.