John Edwards Conway (September 1, 1934 - June 1, 2014) was 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, remaining in the U.S. Air Force Reserve from 1960 to 1970. He received an LL.B. from Washburn University School of Law in 1963, and entered private practice in Santa Fe, New Mexico until 1964, and then in Alamogordo, New Mexico until 1980.