In this paper, the convertible undeniable multi-signature scheme is proposed. An undeniable signature scheme has a property that a verifier can not authenticate the signature of the document without help of the signer. An undeniable multi-signature scheme also has similar property that the signature of the document can not be verified without co-operation of all participating signers. The proposed convertible undeniable multi-signature scheme can convert the undeniable multi-signature to the ordinary multi-signature. The authenticity of confidential document can only be verified with co-operation of all signers. If the document is no longer confidential, it can be opened to public use by converting the undeniable multi-signature on the document to the ordinary one. The proposed scheme satisfies undeniable property and can be applied to copyright protection of digital contents made by many authors.