John Edwards Conway (born 1934) is a United States federal judge.
Born in Joplin, Missouri, Conway received a B.S. from U.S. Naval Academy in 1956 and was a U.S. Air Force Lieutenant from 1956 to 1960. He was in the U.S. Air Force Reserve from 1960 to 1970, receiving an LL.B. from Washburn University School of Law in 1963, and working in private practice in Santa Fe, New Mexico until 1964, and then in Alamogordo, New Mexico until 1980. He was a city attorney of Alamogordo, New Mexico from 1966 to 1972. He was a New Mexico state senator from 1970 to 1980. He was a Minority leader, New Mexico State Senate from 1972 to 1980. He was in private practice in Albuquerque, New Mexico from 1980 to 1986.
Conway was a federal judge on the United States District Court for the District of New Mexico. Conway was nominated by President Ronald Reagan on May 14, 1986, to a seat vacated by Bobby Ray Baldock. He was confirmed by the United States Senate on June 13, 1986, and received his commission on June 16, 1986. He served as chief judge from 1994-2000. He assumed senior status on September 1, 2000.