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The anonymity and dynamic characters of p2p (peer to peer) system makes p2p become hotbed with selfish and vicious action. In order to solve the problem of node cheating caused by high dynamic property of P2P, this paper designs a security trust model -- BGTR based on the idea of probability model and fuzzy mathematics. The scheme adopts a new query method that the inquiry peer initiates the calculated trust value of the queried peer, and combines it with the global trust value calculated at the same time by the queried peer. The theory of uncertainty is also introduced into three aspects of the model to make more adaptive to real situation, which includes Bayesian distinguish model, the triad of trust value, and the transaction times and interval of time. The BGTR model has been tested in effectiveness of transaction success rate caused by the risk index, and in the properties of anti-interference. The P2P network with BGTR trust model has proved higher security and has better performance to resolve problems of impostors, malicious collective attacks and free-rides.