Network Covert Channels (NCC) enhance covertness by concealing the existence of information transmission. However, traditional NCCs remain vulnerable to traffic analysis. Once NCC is detected, adversaries can breach anonymity by uncovering users' network identities and even communication relationships. While certain indirect NCCs offer limited anonymity to protect the identity of at most one party and the relationship, this level proves insufficient. This paper proposes ANCC, an innovative Anonymous Network Covert Channel that is the first to achieve comprehensive anonymity for the sender, the receiver and the communication relationship. By leveraging the Tor network's Hidden Service Directories (HSDirs) as intermediate nodes, Tor-based ANCC modulates covert information through the publication and retrieval statuses of hidden services distributed on multiple HSDirs. This mechanism allows ANCC traffic to blend seamlessly into legitimate Tor traffic, ensuring both robust covertness and high-level anonymity. Theoretical analysis demonstrates that even against a powerful adversary compromising fifty intermediate nodes, the detection probability remains below 0.25%, with the risk of identity or relationship exposure staying negligible (under 0.0021% and 0.00002% respectively). Additionally, the multiple HSDirs supporting parallel transmission enhance the channel capacity and error correction encoding strengthens the robustness. Extensive evaluation within the real-world Tor network demonstrates a transmission accuracy exceeding 99.6% and a channel capacity of around 3 Kbps, proving its effectiveness for practical applications.