Based on the ring signature technology, the multi-receiver ID-based anonymous signcryption (MIBAS) is proposed, and its goal is to protect the privacy of the sender or so-called signer. In an MIBAS scheme, every receiver can verify whether the sender is a member of a trusted group and thus ensure the reliability of the message source, but he could not get the real sender. However, MIBAS paid no attention to privacy of the receivers and has not taken the privacy of the receivers into account during its design. Our analyses show that there widely exist the receiver privacy exposure and decryption unfairness problems in the existing multi-receiver ID-based signcryption schemes. Motivated by these concerns, a new multi-receiver ID-based anonymous signcryption (nMIBAS) is proposed to protect the identity of the receivers. The nMIBAS scheme can not only solve the problem that the existing schemes cannot protect the privacy of receivers, but also meet the fairness of decryption to prevent the possible cheating behavior of the sender effectively. Analysis shows that this scheme is a secure and effective signcryption scheme.