In this paper, a new method is proposed for fuzzy structural reliability analysis; it considers epistemic uncertainty arising from the statistical ambiguity of random variables. The proposed method, namely, fuzzy dynamic-directional stability transformation method, includes two iterative loops. An internal algorithm performs the reliability analysis using the dynamic-directional stability transformation method and an external algorithm performs the fuzzy analysis by applying the alpha-cut level optimization method based on the genetic algorithm. Implementation of the proposed method, which solves some nonlinear performance functions, indicates the efficiency and robustness of the dynamic-directional stability transformation method, as compared to other first order reliability methods.