Peter Hugoe Matthews, FBA (born 1934) is a British linguist and historian of linguistics. He is a fellow of St John's College, Cambridge, and was formerly Professor and Head of the Department of Linguistics at the University of Cambridge (1980–2000). He was elected a Fellow of the British Academy in 1985.
Matthews is perhaps best known for his writings on linguistic morphology. He has published two monographs on the subject.
Matthews was an early follower of Noam Chomsky, but lost enthusiasm for the "generative enterprise" during the 1960s. He has described the Chomskyan revolution as "the Best Thing that has happened to linguistics in the past 2500 years". But he also writes, that dominance of various Chomskyan ideas is not "a Good Thing, and I would not be disappointed if my study of their origins were to lead more scholars to question them".