© 2017 Elsevier B.V.An identity-based conditional proxy re-encryption scheme (IB-CPRE) allows a semi-trusted proxy to convert a ciphertext satisfying one condition, which is set by the delegator, under one identity to another without the necessity to reveal the underlying message. In ICISC 2012, Liang, Liu, Tan, Wong and Tang proposed an IB-CPRE scheme, and left an open problem on how to construct chosen-ciphertext secure IB-CPRE supporting OR gates on conditions. In this work, we answer this aforementioned problem by constructing an identity-based conditional proxy re-encryption scheme with fine grain policy (IB-CPRE-FG). In an IB-CPRE-FG scheme, each ciphertext is labeled with a set of descriptive conditions and each re-encryption key is associated with an access tree that specifies which type of ciphertexts the proxy can re-encrypt. Furthermore, our scheme can be proved secure against adaptive access tree and adaptive identity chosen-ciphertext attack.