In the big data background, data privacy becomes more and more important when data leakage and other security events occur more frequently. As one of the key means of privacy protection, anonymous communication attracts large attention. Aiming at the problems such as low efficiency of message forwarding, high communication delay and abusing of anonymity, this paper presents an identity-based traceable anonymous communication model by adding a preprocessing phase, modifying the ciphertext structure and increasing the controllability of anonymity. Firstly, a new identity-based signature algorithm is proposed, and its security is proved via existential unforgeability against chosen-message attacks (EU-CMA). The signature algorithm is further applied to the anonymous communication model to implement the controllability of revocable anonymity. Secondly, by adding a preprocessing Setup phase, the operations of identifications distribution and user authentication are launched before the anonymous communication phase starts, and this practice significantly improves the efficiency of the anonymous communication model. Finally, by adding the hash value of the message and the user identification as the message authentication code, we design a new ciphertext structure, which can efficiently guarantee the integrity of the ciphertext. Performance analysis and simulation results show that the proposed anonymous communication model has high message forwarding efficiency and better security and controllability of anonymity.