Concord is a census-designated place in Appomattox and Campbell counties in the U.S. state of Virginia. The population as of the 2010 census was 1,458. This town was a stop on the Southside Railroad in the mid-nineteenth century. This became the Atlantic, Mississippi and Ohio Railroad in 1870 and then a line in the Norfolk and Western Railway and now the Norfolk Southern Railway. Sylvia Trent-Adams grew up on a farm in Concord.