Abstract: An analytical moment-based method for calculating structural first failure times under nonGaussian stochastic behaviour is proposed. In the method, a power series that is constant can be obtained from response moments (skewness, kurtosis, etc.) was used firstly to map a non-Gaussian structural response into a standard Gaussian process, then mean up-crossing rates, mean clump size and the initial passage probability of a critical barrier level by the original structural response were estimated. Finally, the formula for calculating first failure times was established on the assumption that corrected up-crossing rates are independent. An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Gaussian model.