The Formula 1 star has been working on material at a west London studio, but has no plans to release the R&B tracks.
He apparently wanted to produce his own material since he is a huge music fan and has spent a fortune hiring the same studio used by the likes of Robbie Williams and Kylie Minogue.
A source told The Sun: "Not many people know Lewis has been making music in his spare time.
"He's really into his R&B and has been cutting lots of songs that fit in with his taste. At the moment he's fully focused on F1 so it's unlikely any of the tracks will be made public.
"But he's had good feedback from the few people who have heard them."
Hamilton, who is allegedly trying to win back ex-girlfriend Nicole Scherzinger, hired the complete studio complex so no one spotted him.