A proxy signature enables the original signer to delegate his/her signing right to a proxy entity, who signs a message on behalf of the original signer. The ID-based proxy signature scheme can be viewed as the combination of a general proxy signature and an ID-based signature. In this paper, we design a formal model for the security of ID-based proxy signature schemes. Recently, Boldyreva et al.[6]show that an aggregate signature scheme is secure, then so is the proxy signature scheme based on this aggregate signature scheme. Using this result and ID-based aggregate signature scheme of Cheon, Yoon and Kim[15], we propose a secure ID-based delegation-by-certificate proxy signature scheme.