G-Man (short for Government Man) is a slang term for Special agents of the United States Government. It is specifically used as a term for a Federal Bureau of Investigation (FBI) agent. In FBI mythology, the nickname is held to have originated during the arrest of gangster George "Machine Gun" Kelly by agents of the Bureau of Investigation (BOI), a forerunner of the FBI, in September 1933. Finding himself unarmed, Kelly supposedly shouted "Don't shoot, G-Men! Don't shoot, G-Men!"[1] This event is dramatized in the 1959 film, The FBI Story. The earliest cite in OED for the American usage is 1930 from a book on Al Capone by FD Pasley.
With the popularity of "Film Noir" and gangster films during the 1940s and 50s, 'G-Men' became a popular slang term for the FBI.