A novel quantitative network trust evaluation algorithm for peer-to-peer computing security system is proposed. The main features of the proposed model include time decay function and entity union function. First of all, the current representative algorithms of network trust evaluation are summerized and classified systematically. And the significant research fields of the related algorithms are categarized and the definition of trust related terminology is given. In this paper, an algorithm with trust time correct function, domain trust correct function and the definition of accuracy is constructed. Four features of the algorithm: time decay feature, history experience related feature, new entity award feature and union feature, are proved. At the same time, a natural trust decay curve is described and eight typical domain features are given. The experiments are also designed to evaluate the correctness and performances of the proposed algorithm, the results of the experiments are compared with Azzedin algorithm, and the results prove the sound performance and correctness of the algorithm. Finally, some related future research fields of the paper are pointed out.