The 1960 Utah Redskins football team was an American football team that represented the University of Utah as a member of the Skyline Conference during the 1960 NCAA University Division football season. In their third season under head coach Ray Nagel, the Redskins compiled an overall record of 7–3 with a mark of 5–1 against conference opponents, placing third in the Skyline. Home games were played on campus at Ute Stadium in Salt Lake City. Utah was led on the field by senior quarterback Terry Nofsinger.