Martin Leslie Cook was born on 1 April 1923, the second child of J. Leslie and Bertha Cook. Throughout his childhood in Purcellville, Virginia, he was fascinated with mechanics and airplanes. One of the most memorable events of his youth was a plane ride his grandfather, Joe Cook, paid for him and two sisters to take when he was five or six. Martin was valedictorian in the 1940 graduating class of Loudoun County Training School in Leesburg, the only African-American secondary school in Loudoun County. After graduation, he worked as a painter and carpenter with his father in Purcellville.

In November 1942, Cook enlisted in the army and passed the entrance examination for the U.S. Army Aviation Cadet Program, which allowed him to enroll in Tuskegee Army Flying School, the recently-created military aviation school for African-Americans. He graduated in April 1944, received his Army commission and was assigned to 477th Bombardment Group, 618th Bomb Squadron. However, Cook never saw combat. While en route to France in the spring of 1945, an armistice was signed and his services as a fighter pilot were no longer needed. He later remembered this as the biggest disappointment of his life.

Cook resigned from the Army Air Corp at the end of November 1945 to pursue a degree in aeronautical engineering from The Catholic University of America (CUA) in Washington, D.C. While enrolled in school, he worked at Fluid Mechanics Division of the National Bureau of Standard. After graduating in 1953, Cook was employed for thirty-two years with the U.S. Navy in the Department of Defense as an aeronautical engineer. He retired at the rank of Lieutenant Colonel from the U.S. Air Force Reserve in 1976, and from the Department of Defense in 1983. In retirement, he continued to pursue his passion for mechanics, including working on his automobiles. Cook was an avid reader and, at the time of his death, was conducting research in the National Archives for a book on the careers of Tuskegee graduates.

While attending CUA, he boarded at the home of his future wife's sister. On 14 November 1953, he and Evelyn Alice Lucas married. They had four children: Daryl Andrew Cook, Deborah Leslie Cook Moten, Doreen Lynn Cook Hope, and Martin Leslie Cook, Jr. Cook was an active member of the Seventh Day Adventist church. Among the congregations to which he belonged were Brotherhood and Capital Memorial, both in Washington, D.C. Martin Leslie Cook died on 24 October 2002, and was interred at Arlington National Cemetery on 6 December 2002.