A proxy re-encryption scheme enables a proxy to re-encrypt a ciphertext under a delegator’s public-key and designate it to a delegatee. Weng et al. introduced the notion of conditional proxy re-encryption (or C-PRE, for short), whereby only the ciphertext satisfying one condition set by the delegator can be transformed by the proxy and then decrypted by delegatee. Nonetheless, they left an open problem on how to construct CCA-secure C-PRE schemes with anonymity. In this paper, we first formalize the notion of anonymous condition CCA-secure PRE and present a respective security model. Then, we answer the question posed by Weng et al. affirmatively by presenting a new and efficient construction of anonymous conditional proxy re-encryption (C-PRE) scheme without requiring random oracle.