Robert Hugh Willoughby (born June 6, 1921) is an American classical flute player and flute teacher. He plays both Baroque and modern flute. He has been described by Flute magazine as the "American grandmaster of the flute". Willoughby taught for many years at Oberlin College, where he was the first Robert Wheeler Professor of Performance. He taught for ten years at the Peabody Institute, and now teaches at the Longy School of Music of Bard College. In 1996 he received a Lifetime Achievement Award from the National Flute Association.