In a multi-receiver encryption system, a sender chooses a set of authorized receivers and sends them a message securely and efficiently, as the message is well encrypted and only one ciphertext corresponding to the message is generated no matter how many receivers the sender has chosen. It can be applied to video conferencing systems, pay-per-view channels, remote education, and so forth. Due to privacy considerations, an authorized receiver may not expect that his identity is revealed. In 2010, anonymous multi-receiver identity-based (ID-based) encryption was first discussed, and furthermore, many works on the topic have been presented so far. Unfortunately, we find that all of those schemes fail to prove the chosen ciphertext attacks (CCA) security in either confidentiality or anonymity. In this manuscript, we propose the first anonymous multi-receiver ID-based authenticated encryption scheme with CCA security in both confidentiality and anonymity. In the proposed scheme, the identity of the sender of a ciphertext can be authenticated by the receivers after a successful decryption. In addition, the proposed scheme also is the first CCA-secure one against insider attacks. Moreover, only one pairing computation is required in decryption.