The open, sharing and anonymous nature of peer-to-peer (P2P) networks has made it popular in many large-scale distributed applications over the Internet. However, due to the fact that resource-sharing activity of a peer in P2P networks is a volunteer behavior and it is not responsible for its irresponsible bartering history, the trust relationship between participants can not be constructed only on the traditional trust mechanism. A feasible resolution derived from the trust relationship in social networks, is to establish a reputation based global trust model. The previous work about the global trust model is mostly based on the assumption that the peer with higher trust value will provide more honest feedbacks, and make the quality of feedback of a peer be approximately equal to that of service of the peer. However, this is not always true. To solve this problem, this paper proposes a robust feedback credibility (FC) based distributed P2P global trust model (FCTrust), to quantify and evaluate the trustworthiness of participants, and gives the mathematic analyses and distributed implementation method. Theoretical analyses and simulation experiments show that FCTrust has advantages in combating various malicious behaviors such as dishonest feedbacks from malicious peers, the collusion and the strategic attacks to the trust model itself, over the current global trust models, and demonstrates more robustness and effectiveness.