Willis, 57, wants to leave to his huge digital music collection to his daughters, Rumer Scout, 20 and 18-year-old Tallulah from ex-wife Demi Moore, after he dies but iTunes customers are only allowed to borrow tracks rather than own them outright, reported Sun online.
"You can't resell downloads to friends - and are not allowed to leave them in your will. It's great that Bruce Willis is challenging it," said Jim Killock from Digital campaigners Open Rights Group.
The 'Sixth Sense' star is thought to be thinking of asking his legal team to suggest to Apple that family trusts could be the holders of his downloaded music.