Proxy re-encryption is a cryptographic primitive which enables a ciphertext encrypted under a delegator's public key to be translated into a ciphertext of a delegatee by a semi-trusted proxy. Conditional proxy re-encryption (CPRE) is a variant of proxy re-encryption which allows the delegator to control the delegation of decryption rights with certain conditional value. The existing CPRE schemes left an open problem about how to construct CCA-secure CPRE schemes supporting Boolean predicates over conditions. In this paper, we propose attribute-based CPRE (AB-CPRE) in which the delegator could implement attributed-based control on the delegation of decryption rights by setting conditions in the form of access structure and attribute set. AB-CPRE is suitable for applications where fine-grained control of the decryption delegation is necessary. We formalize definitions and security notions for AB-CPRE and prove that the proposed scheme is chosen-ciphertext secure under the 3-Quotient Decision Bilinear Diffie-Hellman (3-QDBDH) assumption.