Cipher text-Policy Attribute-Based Proxy Re-Encryption (CP-ABPRE) extends the traditional Proxy Re-Encryption (PRE) by allowing a semi-trusted proxy to transform a cipher text under an access policy to the one with the same plaintext under another access policy (i.e. attribute-based re-encryption). The proxy, however, learns nothing about the underlying plaintext. CP-ABPRE has many real world applications, such as fine-grained access control in cloud storage systems and medical records sharing among different hospitals. Previous CP-ABPRE schemes leave how to be secure against Chosen-Cipher text Attacks (CCA) as an open problem. This paper, for the first time, proposes a new CP-ABPRE to tackle the problem. The new scheme supports attribute-based re-encryption with any monotonic access structures. Despite our scheme is constructed in the random oracle model, it can be proved CCA secure under the decisional q-parallel bilinear Diffie-Hellman exponent assumption.