Early in the war Burnham became lieutenant colonel of the 6th Maine Infantry on July 16, 1861. He was promoted to the rank of colonel on December 12 of that year. He served with the Army of the Potomac in the Peninsula Campaign, starting out in Brig. Gen. Winfield S. Hancock's brigade in a division of the IV Corps under Brig. Gen. William F. Smith. This division later became part of the VI Corps. At the Battle of Crampton's Gap and the Battle of Antietam, Burnham led his regiment in the 1st Brigade, 2nd Division, VI Corps under Hancock. He led the same regiment under Brig. Gen. Calvin E. Pratt at the Battle of Fredericksburg, where the brigade was only lightly engaged.