Considering the defects of traditional Failure Modes,Effect and Criticality Analysis (FMECA), a criticality analysis method based on fuzzy Bayesian networks was proposed. This approach combined the fuzzy theory with Bayesian network techniques, and fuzzy judgments of experts were described using triangular fuzzy numbers which were transformed into forms of fuzzy subsets of ranking through mapping of fuzzy sets. The fuzzy rules with belief structure were used to represent the relationship between the properties and hazards of the failure modes. The Bayesian network inference algorithms were used to synthesize the fuzzy rules of belief structure, and the hazard degree in the form of fuzzy subsets was obtained by Bayesian inference, through defuzzification calculation, a precise value of fault hazard ranking was gained to determine the hazard degree of the failure mode. The experimental results show that the proposed method is able to improve the accuracy and application range of the traditional analysis method.