Greenup County is a county located along the Ohio River in the northeastern part of the U.S. state of Kentucky. As of the 2020 census, the population was 35,962. 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.

Christopher Greenup was an American politician who served as a U.S. Representative and the third Governor of Kentucky. Little is known about his early life; the first reliable records about him are documents recording his service in the Revolutionary War where he served as a lieutenant in the Continental Army and a colonel in the Virginia militia.