Multi-proxy signature schemes are quite useful tools while a signer requires delegating his signing right to a group of proxy signers. There are two main types of formal security models of multi-proxy signatures. However, they have deficiencies, respectively. One of them is complicated, and does not model the chosen warrant attacks; the other model does have the incomplete definition of adversary. Meanwhile, there is so far no provably secure identity-based multi-proxy signature scheme. In this paper, we give a formal security model of the identity-based multi-proxy signature schemes, and propose an identity-based multi-proxy signature scheme. Our security model compensates for deficiencies in existing models. It defines more powerful adversary capacity, formalizes the behaviors of the adversaries, and adopts simple and clear proof structure. The proposed identity-based multi-proxy signature scheme is based on the well-studied CDH (computational Diffie-Hellman) assumption, and is proven existentially unforgeable against chosen message/warrant attacks in our security model. In addition, we present that there are three security flaws in a recent proposed identity-based multi-proxy signature scheme and in its security model. Comparative analysis shows that the new security model is more complete, and the new multi-proxy signature scheme is a real and provably secure identity-based cryptosystem in the standard model.