Authentication and confidentiality, as well as sender and receiver anonymity are essential in broadcast communication. In this paper, an anonymous hybrid signcryption scheme with multi-receiver is proposed using identity-based cryptography. The proposal does not contain receiver's identity list, and the identity of sender is included in an identity set. Thus, it not only obtains the receiver's anonymity, but also achieves the sender's anonymity. Additionally, the proof of security and the analysis of correctness demonstrate that the scheme is secure and effective. Compared with the pre-existing schemes, the proposal enjoys better performances in many perspectives, including confidentiality, unforgeability, higher anonymity of sender and receiver and public verifiability. Moreover, the presented method can be improved to develop an efficient construction of hybrid signcryption scheme with multi-message and multi-receiver, which can obtain these security properties, such as sender and receiver anonymity, public verifiability and non-repudiation. Finally, the new variant can achieve the requirement of sending multi-message in broadcast communication.