Existing ID-based multi-receiver signcryption schemes presents some security problems. For example, the identities of receivers can be revealed and the receivers do not have fairness in decryption. In order to avoid those problems, this paper proposes a fair ID-based multi-receiver anonymous signcryption scheme. The new scheme can not only solve the problem that the existing schemes can not protect the privacy of receivers, but also meet the fairness of decryption to effectively prevent possible cheating behavior of the sender. It then proves the confidentiality and unforgeability under of the scheme the bilinear Diffie-Hellman assumption and the computational Diffie-Hellman assumption. Simultaneity, the correctness and the performance of this scheme are analyzed. It concludes that this scheme is a secure and effective public-key signcryption scheme and can solve the problems of the receivers' identity exposure and unfairness decryption. Therefore, the new scheme has very important applications, especially it can be used to broadcast sensitive information in unsafe and open network environment.