The Peer-to-Peer systems (P2P) are a center of interest in the community of distributed systems, since their advantages in the adaptability and the robustness with regard to the traditional architectures client / server. Unfortunately, the anonymous and open nature of these systems involves an almost impossible surveillance of the network and offers nearly an ideal environment for the spread of the inauthentic files. To offer a more extensive vision of the network and to limit the malicious interactions between different peers of the network, we present a new model of trust management that considers the direct trust based on the peer's history of uploads and the indirect trust which is calculated after constructing trust paths