Fannin County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 33,915. The county seat is Bonham. The county was named for James Fannin, who commanded the group of Texans killed in the Goliad Massacre during the Texas Revolution. The county was created in 1837 and organized the next year.Fannin County is a part of the Texoma region.