A proxy re-encryption scheme allows the proxy to transform ciphertext computed under one public key into the different ciphertext that can be decrypted by using another public key. Recently, many identity-based proxy re-encryption schemes have been proposed. However, all of these schemes are only proved secure in the random oracle not in the standard model. In this paper, Based on Waters's identity based encryption, an identity based proxy re-encryption scheme is proposed that is proved fully secure without the random model. The proposed scheme's security can be reduced to the decision Bilinear Diffie-Hellman assumption.