The hinged slab bridge is widely used in medium- and small-span bridges because of its simple structure and convenient construction. However, hinge joints damage is the main defect of this kind of bridge, and it is difficult to express the deterministic damage degree of hinge joints in the detection process. A system reliability evaluation method considering fuzzy detection information of hinge joints damage and member failure credibility is proposed in this paper. Firstly, the membership function is used to quantitatively express the fuzzy detection information of hinge joints, and the fuzzy variable is transformed to an equivalent random variable. Secondly, the functional relationship between the transverse distribution coefficient and hinge joints damage is constructed by the modified hinge-jointed plate method and response surface method, and the reliability of the member considering the fuzzy detection information of hinge joints damage is calculated by the first-order second-moment method (FOSM). Then, the failure credibility is introduced to represent the different possibilities of system failure caused by member failure, and a system reliability assessment method of different failure criteria considering member failure credibility is established based on copula theory. Finally, the applicability of the proposed method is verified by taking the reinforced concrete hinged slab bridge as a numerical example.