At present, reliability assessment plays an important role in power systems. When the component failure probabilities are interval valued, common methods fail to achieve reasonable interval reliability assessment result of power systems. In this paper a novel approach based on the belief universal generating function (BUGF) is proposed to calculate the reliability indexes of power systems. Instead of giving a single-valued assessment result, a belief function and a plausibility function are exploited to calculate the lower and upper bounds of the loss of load probability (LOLP), the loss of load expectation (LOLE), the expected unsupplied load (EUL) and the expected unsupplied energy (EUE) in UGF, respectively. The proposed approach can track the correlation of the original data well and keep it to the end of the calculation. By using BUGF compared to other common methods to calculate the interval LOLP, LOLE, EUL, and EUE of IEEE-RTS 79, the results show the BUGF method can track the correlation of the original data well, and can get narrower and more accurate interval reliability indexes of the power generation system, which illustrates the effectiveness of the proposed approach.