You are likely thinking of "The Greatest Show on Earth" (1952), which features Charlton Heston and a large cast including James Stewart. It is a classic circus movie, but does not star John Wayne.
John Wayne did star in a movie called "Circus World" (1964), but it is not the same movie as "The Greatest Show on Earth". "Circus World" was a big budget film, however, it was not well-received and is considered one of Wayne's lesser films.
Both movies are available on DVD.