The 1891 Army Cadets football team represented the United States Military Academy in the 1891 college football season. In the first full season of Army football (Army had played a single game in 1890), the Cadets compiled a 4–1–1 record and outscored their opponents by a combined total of 80 to 73. The Cadets opened the season with a 10–6 victory over Fordham – the first win in Army football history. In the final game of the season, the Cadets defeated the Midshipmen by a 32 to 16 score in the second annual Army–Navy Game.