Record label boss James Fitzpatrick launched a ‘crowd funding’ appeal at the weekend on website Kickstarter.
Just four days later, and following a story in The Yorkshire Post, the amount pledged towards the £25,000 target has already topped £18,000.
As the original master tapes to the 1979 film were reportedly lost Mr Fitzpatrick wants to produce a new music CD with the Prague Philharmonic Orchestra.
A soundtrack released at the time was missing several key moments from the score, including the famous Bond theme music.
Hundreds of fans have pledged cash, ranging from £20 to over £1,000.
Geoff Leonard, an author who has co-written two biographies on Barry, pledged a large sum towards the project.
He said: “I’ve been a fan of John Barry since the early 1960s and welcome any attempt to release more of his music. To help make Moonraker happen I pledged a considerable amount of cash!”
The deadline for reaching the target is February 9. Barry, who composed soundtracks for 11 Bond films, died in 2011.