Henry P. Smith III (September 29, 1911 – October 1, 1995) was an American politician and Republican member of the United States House of Representatives from New York. Smith was born in North Tonawanda, New York. He graduated from Dartmouth College in 1933 and Cornell Law School in 1936. He was mayor of North Tonawanda, New York from 1961 until 1963. He was elected to Congress in 1964 after longtime congressman William E. Miller gave up the seat to run as Barry Goldwater's running mate. He served from January 3, 1965, until he retired from Congress January 3, 1975 after opting not to seek re-election.