Traffic reliability is a crucial property of the transportation system, showing its ability to resist traffic jams or collapse. Traditional traffic reliability analysis only considers stochastic uncertainty but neglects epistemic uncertainty, which widely exists in the traffic network and leads to an underestimation of traffic failure. In this paper, we introduce uncertainty theory to model epistemic uncertainty, thereby developing a belief reliability analysis method for transportation systems based on the traffic performance margin. We established an uncertain percolation semi Markov (UPSM) model to describe the essential physical characteristics of the traffic accidents considering both stochastic and epistemic uncertainty. And the uncertain percolation model is utilized to describe the traffic performance degradation and the semi Markov process is developed to represent the influence of random emergency events. According to the traffic failure propagation process, a simulation method for calculating belief reliability is proposed. Finally, a case study was given to illustrate the proposed method.