Graham Newell Fitch (December 5, 1809 – November 29, 1892) was a United States representative and senator from Indiana, as well as a brigade commander in the Union Army during the American Civil War.

Born in Le Roy, New York, he attended Middlebury Academy and Geneva College.

He studied medicine and completed his medical course at the College of Physicians and Surgeons, and commenced practice in Logansport, Indiana, in 1834.

After the Civil War erupted and President Abraham Lincoln called for 100,000 volunteers to put down the rebellion, Fitch raised the 46th Indiana Infantry.

During the battles of New Madrid and Island Number Ten, Fitch commanded the 2nd Brigade of Brigadier General John M. Palmer's infantry division.