By taking into consideration the effect of uncertainty of failure rate and weather condition on reliability evaluation of power system, based on the piece-wise model of transmission line, this paper presents a new reliability assessment model based on the interval probability theory to solve the uncertainty problem. The method uses interval arithmetic and state enumeration method to calculate interval-valued reliability indices of IEEE-RBTS. Furthermore, a large overestimate of boundaries in the interval arithmetic can be improved by affine arithmetic. The result shows that the weather condition will affect the reliability evaluation of the transmission system greatly, and the reliability indices in form of interval number also give the size of the uncertain part, which proves the efficiency and validity of the proposed method. This work is supported by National Natural Science Foundation of China (No. 51007017).