Morehead is a city of Rowan County, Kentucky, United States. The population was 5,914 at the 2000 census. The city is named for Gov. James T. Morehead. Most of Rowan county now has the ZIP code 40351 or 40313. It is the county seat of Rowan County. Morehead State University is located here. It was also the focal point of the Rowan County War.