Greenup County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 36,910. The county was founded in 1803 and named in honor of Christopher Greenup. Its county seat is Greenup.Greenup County is part of the Huntington-Ashland, WV-KY-OH Metropolitan Statistical Area (MSA), as well as the Charleston-Huntington-Ashland, WV-OH-KY Combined Statistical Area. As of the 2010 census, the MSA had a population of 287,702.