Abstract: An important challenge regarding entity’s trust valuation in open computing systems, such as P2P systems, grid, semantic web, and ad hoc networks, etc., is how to cope with trust transitivity and trust aggregation in the encounter of a large number of malicious entities existing in the system efficiently．However，the trust models employed by the existing systems have some certain disadvantages in the accuracy and reliability of trust metric. Firstly, they ignore the feedback trust measurement on the direct recommender in the process of trust transitivity. Secondly, they contain the problems of information loss or repetitive calculation for their limits in analysis and disposal of the dependent relationships among referral chains. The above reasons also make the deviation between the trust measurement result and actual trust degree increasing. A novel evidential trust model, namely GTETM, a graph theory based evidential trust model, is presented in this paper, and the problems existing in current methods for transferring and aggregating trust relationships are addressed by combning D-S evidence with graph theory. It can be seen from the simulation results that compared with the existing trust metrics, GTETM is more robust on defending against malicious attacks for various strategy cheating and collusion, and has more remarkable enhancements in the accuracy of trust metric.