The 1963 Grambling Tigers football team represented Grambling College (now known as Grambling State University) as a member of the Southwestern Athletic Conference (SWAC) during the 1963 NCAA College Division football season. Led by 21st-year head coach Eddie Robinson, the Tigers compiled an overall record of 5–3–1 and a mark of 3–3–1 in conference play, and finished tied for fourth in the SWAC.
