A proxy re-encryption scheme (PRE) allows a semi-trusted proxy to convert a ciphertext encrypted under one key into a ciphertext encrypted under another key without leaking the underlying plaintext. In the process of the arithmetic processing, proxy should be able to learn as little information about the plaintext as possible. Conditional proxy re-encryption (CPRE) is a new cryptography primitive which only those ciphertexts satisfying one condition set by the delegator can be re-encrypted correctly by the proxy. In this paper, we first propose the formal definition and security model of certificate- based conditional proxy re-encryption. Further, we combine the conditional proxy re-encryption with certificate-based encryption and present a certificate-based conditional proxy re-encryption scheme. The proposed scheme is proved secure against chosenciphertext attack (CCA) in the random oracle model. Security of the scheme is reduced to the intractability of the bilinear Diffie-Hellman problem. Finally, we give the efficiency analysis of our scheme.