A fundamental problem in a pure Peer-to-Peer (P2P) file sharing system is how to protect the anonymity of peer nodes when providing efficient data access services. Most of existing work mainly focus on how to provide the initiator anonymity, but neglect the anonymity of the responder. In this paper, we propose a multicast-based protocol, called Mapper, for efficient file sharing with mutual anonymity. By seamlessly combining the technologies of multi-proxy and IP multicast together, the proposed protocol guarantees mutual anonymity during the entire session of file retrieval. Furthermore, Mapper replicates requested files inside the multicast group, so file distribution can be adjusted adaptively and the cost for multicast can be further reduced. Results of both simulations and theoretical analyses demonstrate that Mapper possesses the merits of scalability, reliability, and high adaptability.