Fuzziness and randomness are two different uncertainties , and often axist in one engineering problem.Based on the possibility theory ,a procedure for reliability calculation of the structures that contain both random variables and fuzzy variables is presented in the paper. The possibility distribution of fuzzy failure probabilily of structures can be given by the proposed model. Being different from some common models , the failure probability of fuzzy-random structures is taken as fuzzy variable , which may indicate the real safety state of structures objectively.The computations of examples illustrate the feasibility and application of the proposed method.