Parrott is a census-designated place in Pulaski County, Virginia, United States. The population as of the 2010 Census was 435.The town was named after John Henry Parrott, Jr.. Parrott started the Pulaski Anthracite coal mine in 1902 and was the mine's general manager and probable shareholder.Parrott is bordered by the New River which is the oldest river system on the North American continent and second only to the Nile River in Africa as the oldest river in the world. It flows northward rather than southward like most of the other major rivers along the eastern seaboard.