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.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, we propose a secure ID-based delegation-by-certificate proxy signature scheme.