Glennon is a surname. Notable people with the surname include:
James H. Glennon (1857-1940), Rear Admiral in the United States Navy
John Alan Glennon (born 1970), American geographer and explorer
John J. Glennon, Roman Catholic Archbishop of the Archdiocese of Saint Louis, from 1903 to his death in 1946
Michael Glennon (c. 1944 – 2014), Australian Roman Catholic priest and convicted child molester
Mike Glennon, American football quarterback
Sean Glennon, American football quarterback
