Old Horry County Courthouse, now known as Conway City Hall, is a historic court house building located at Conway in Horry County, South Carolina. It was built between 1824 and 1825 and reputedly designed by Robert Mills (1781-1855). It is a two story Classical Revival brick building. It features an extended pediment supported by Doric order columns that shelters a second story portico which does not extend the full width of the façade. It was listed on the National Register of Historic Places in 1971.