According to the situation of randomness and fuzziness existing in the actual project, this paper proposed a reliability-credibility model based on fuzzy theory, possibility theory and credibility theory. At firstly, a reliability-possibility distribution curve was constructed by the traditional stress-strength interference model, then, a reliability distribution function was established based on this. This model built a bridge between credibility and reliability in handling randomness and fuzziness. The research results show that the model can hand the situation of random information and fuzzy information coexistence well, and the acceptable level of reliability and the most credible reliability value can be reflected directly in the reliability-credibility distribution curve. Compared with other methods, it obtains more reliability information, accords with the actual engineering situation and guides reliability engineering design much better.