The songs, dating back to the 1980s, will be released on a compilation album, May told BBC radio.
Lead singer Mercury died of AIDS-related pneumonia in 1991. Four years later, Queen released "Made In Heaven", their final studio album with the iconic frontman, painstakingly constructing some fresh songs from lines of vocals he left behind.
But May said more tapes in the vault had come to light.
"We found a few more tracks with Freddie singing and all of us playing, and they're quite beautiful, so people will be hearing this work towards the end of the year," the 66-year-old said.
In their current form, the songs do not have the bombastic Queen sound, but May and drummer Roger Taylor -- bassist John Deacon retired in 1997 -- are giving them the band's trademark anthem touch.
"Most of it comes from the eighties when we were in full flight, so it's quite emotional. It's the big, big ballad and the big, big kind of epic sound.
"But knowing how it would've happened if we'd finished it then, I can sit there and make it happen, with modern technology."
May is also working up some rough tracks that Mercury recorded with Michael Jackson in 1983.
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