With increasing application of cloud computing and big data technologies, a large amount of personal information is stored on the Internet, which raises the issue of privacy leakage. In order to protect people's data privacy, this paper firstly presents a new anonymous Identify-Based Encryption (IBE) scheme and shows the proof of its security under the Bilinear Diffie-Hellman Security Assumption. Then, by introducing the anonymous IBE scheme into an anonymous communication model, this paper introduces a new lightweight anonymous communication model for cloud computing, which guarantees the anonymity of system users and the security of messages during the communication in small groups. Our analysis shows that, the proposed communication model cannot only reduce memory consumption and improve message transmission efficiency, but also effectively resist traffic-analysis attacks, node eavesdropping, and finally achieve secure anonymous communication in cloud computing.