Current unstructured peer-to-peer (P2P) systems lack fair topology structures, and take no consideration for malicious behaviors of peers. The main reason is that the topology is not sensitive to peer’s trust, and cannot accommodate heterogeneity of peers over the network. Thus, a feedback credibility based global trust model is presented in this paper. Then, based on the trust model, an adaptive topology evolution mechanism for unstructured P2P networks is proposed. Through this mechanism, trusted peers can migrate to the centric position, while untrusted peers to the edge of the topology, guaranteeing fairness during topology evolution. On the other hand, the mechanism can effectively counter the malicious behaviors of peers, and also has the incentive functionality, which incents peers to provide more high-quality services in order to get more return on services. Analysis and simulations show that, compared with the current topologies, the resulting topology mechanism demonstrates more effectiveness and robustness in combating the selfish or malicious behaviors of peers.