There is epistemic uncertainty on high-reliability components since it is hard to obtain adequate performance data of the components within a short time. The components′ performance distribution parameter is assumed as a fuzzy number, according to the decomposition theorem of the fuzzy set, a performance distribution model based on β- level cut set is built, and a definition of the components′ performance interval in the fuzzy state and a computational method of the fuzzy state probability are provided. The traditional universal generating function is improved, the α-level cut set universal generating function and its algorithm are defined. An assessment method of fuzzy reliability of multistate system in consideration of epistemic uncertainty is proposed, and verification and illustration are conducted with simulation examples in order to reduce the influence on components′ performance analysis and achieve precise estimation of system reliability. This method overcomes the shortcoming that a state information analysis model cannot be accurately built on account of the deficiency of performance distribution information. It can be widely used and has great engineering application value.