One of the most important issues in peer-to-peer networks is anonymity. The major anonymity for peer-to-peer users concerned with the users' identities and actions which can be revealed by any other members. There are many approaches proposed to provide anonymous peer-to-peer communications. An intruder can get information about the content of the data, the sender's and receiver's identities. Anonymous approaches are designed with the following three goals: to protect the identity of provider, to protect the identity of requester and to protect the contents of transferred data between them. This article presents a new peer-to-peer approach to achieve anonymity between a requester and a provider in peer-to-peer networks with trusted servers called suppernode so that the provider will not be able to identify the requester and no other peers can identify the two communicating parties with certainty. This article shows that the proposed algorithm improved reliability and has more security. This algorithm, based on onion routing and randomization, protects transferring data against traffic analysis attack. The ultimate goal of this anonymous communications algorithm is to allow a requester to communicate with a provider in such a manner that nobody can determine the requester's identity and the content of transferred data.