Readers will be able to choose between a young John Lennon cover or one featuring the Beatle in later life.
The Lennon CD will feature classic tracks such as 'Imagine' covered by Madonna, 'I am the Walrus' by Oasis, 'Instant Karma' by Paul Weller, 'Working Class Hero' by Elbow and 'Happy Xmas (War is Over)' by Badly Drawn Boy.
The Beatles star would have celebrated his 65th birthday on October 9, had he not been gunned down on by crazed fan Mark Chapman outside the Dakota Apartment Buildings in New York on December 8 1980.
The special Q issue was made possible after input from Lennon's widow Yoko Ono.
Paul Rees, editor of Q Magazine, said: "The unique access to Yoko Ono is something only Q can get and I'd like to thank Yoko for her input and involvement in helping us celebrate John Lennon's 65th properly."
In the most recent set of ABCs issued on August 18, Q was down 1.4% in the last six months, although it was up 6.3% year on year to 160,310.
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