Braxton County is a county in the central part of the U.S. state of West Virginia. As of the 2020 census, the population was 12,447. The county seat is Sutton. The county was formed in 1836 from parts of Lewis, Kanawha, and Nicholas counties and named for Carter Braxton, a Virginia statesman and signer of the Declaration of Independence. In 2010, the center of population of West Virginia was in northern Braxton County.