It is important to enable peers to represent and update their trust in other peers in open networks for sharing files, and especially services. In this paper, we propose a Bayesian network-based trust model and a method for building reputation based on recommendations in peer-to-peer networks. Since trust is multi-faceted, peers need to develop differentiated trust in different aspects of other peers? capability. The peer?s needs are different in different situations. Depending on the situation, a peer may need to consider its trust in a specific aspect of another peer?s capability or in multiple aspects. Bayesian networks provide a flexible method to present differentiated trust and combine different aspects of trust. The evaluation of the model using a simulation shows that the system where peers communicate their experiences (recommendations) outperforms the system where peers do not share recommendations with each other and that a differentiated trust adds to the performance in terms of percentage of successful interactions.