| John Milton Bryan Simpson | |
| Office: | Senior Judge of the United States Court of Appeals for the Eleventh Circuit |
| Term Start: | October 1, 1981 |
| Term End: | August 22, 1987 |
| Office1: | Senior Judge of the United States Court of Appeals for the Fifth Circuit |
| Term Start1: | June 30, 1975 |
| Term End1: | October 1, 1981 |
| Office2: | Judge of the United States Court of Appeals for the Fifth Circuit |
| Term Start2: | November 3, 1966 |
| Term End2: | June 30, 1975 |
| Appointer2: | Lyndon B. Johnson |
| Predecessor2: | Seat established by 80 Stat. 75 |
| Successor2: | Gerald Bard Tjoflat |
| Office3: | Chief Judge of the United States District Court for the Middle District of Florida |
| Term Start3: | 1962 |
| Term End3: | 1966 |
| Predecessor3: | Office established |
| Successor3: | Joseph Patrick Lieb |
| Office4: | Judge of the United States District Court for the Middle District of Florida |
| Term Start4: | October 29, 1962 |
| Term End4: | November 22, 1966 |
| Appointer4: | operation of law |
| Predecessor4: | Seat established by 76 Stat. 247 |
| Successor4: | Ben Krentzman |
| Office5: | Chief Judge of the United States District Court for the Southern District of Florida |
| Term Start5: | 1961 |
| Term End5: | 1962 |
| Predecessor5: | George William Whitehurst |
| Successor5: | David W. Dyer |
| Office6: | Judge of the United States District Court for the Southern District of Florida |
| Term Start6: | September 26, 1950 |
| Term End6: | October 29, 1962 |
| Appointer6: | Harry S. Truman |
| Predecessor6: | Louie Willard Strum |
| Successor6: | Seat abolished |
| Birth Name: | John Milton Bryan Simpson |
| Birth Date: | 30 May 1903 |
| Birth Place: | Kissimmee, Florida |
| Death Place: | Jacksonville, Florida |
| Education: | Fredric G. Levin College of Law (LLB) |
John Milton Bryan Simpson (May 30, 1903 – August 22, 1987) was a United States circuit judge of the United States Court of Appeals for the Fifth Circuit and the United States Court of Appeals for the Eleventh Circuit and previously was a United States district judge of the United States District Court for the Southern District of Florida and the United States District Court for the Middle District of Florida.
Born in Kissimmee, Florida, Simpson served in the United States Army, as a 1st Lt., in the European Theater from 1943 to 1945. Received a Bachelor of Laws from the Fredric G. Levin College of Law at the University of Florida in 1926. He was in private practice of law in Jacksonville, Florida from 1926 to 1946. He was an assistant state's attorney of the Fourth Florida Circuit from 1933 to 1939. He was a Judge of the Criminal Court of Record in Duval County, Florida from 1939 to 1943. He was a United States Army First Lieutenant from 1943 to 1945. He was a Judge of the Criminal Court of Record in Duval County from 1945 to 1946. He was a Circuit Judge of the Fourth Judicial Circuit Court of Florida from 1946 to 1950.
Simpson was nominated by President Harry S Truman on September 14, 1950, to a seat on the United States District Court for the Southern District of Florida vacated by Judge Louie Willard Strum. He was confirmed by the United States Senate on September 23, 1950, and received his commission on September 26, 1950. He served as Chief Judge from 1961 to 1962. He was reassigned by operation of law on October 29, 1962 to the newly created United States District Court for the Middle District of Florida, to a seat established by 76 Stat. 247. He served as Chief Judge from 1962 to 1966. His service was terminated on November 22, 1966, due to elevation to the Fifth Circuit.
Simpson was nominated by President Lyndon B. Johnson on October 11, 1966, to the United States Court of Appeals for the Fifth Circuit, to a new seat created by 80 Stat. 75. He was confirmed by the Senate on October 20, 1966, and received his commission on November 3, 1966. He assumed senior status on June 30, 1975. He was reassigned by operation of law on October 1, 1981, to the United States Court of Appeals for the Eleventh Circuit. His service was terminated on August 22, 1987, due to his death.
Simpson was noted for his legal decisions during the civil rights demonstrations in St. Augustine, Florida that led directly to the passage of the landmark Civil Rights Act of 1964.
The John Milton Bryan Simpson United States Courthouse in Jacksonville in named in his honor.