Multi-state components, common cause failures (CCFs) and data uncertainty are the general problems for reliability analysis of complex engineering systems. In this paper, a method incorporating fuzzy probability and Bayesian network (BN) into multi-state systems (MSSs) with CCFs is proposed. In particular, basic theories of multi-state BN and fuzzy probability are developed. Moreover, a model integrating CCFs with BN has also been illustrated. In order to incorporate fuzzy probability into MSSs reliability evaluation considering common parent node generated by CCFs, fuzzy probability has to be translated into accurate probability through defuzzification and normalization methods which are both elaborated. In addition, quantitative analysis based on BN is carried out. In this paper, feed system of boring spindle in computer numerical control machine is analyzed as an example to validate the feasibility of the proposed method. It can improve the ability of BN on reliability evaluation of complex system with uncertainty issues.