Abstract: Structural dynamic equations are first transformed intothe form of state equations, which are solved by the precise time integralmethod, and then explicit expressions of structural random responses undernon-stationary excitations are deduced in the time domain. The computationaleffort for such explicit formulation is only equivalent to that for twodeterministic time-history analyses of the structure. Based on the aboveexplicit expressions and combined with the first-excursion failurecriterion, a numerical simulation method is proposed for solving dynamicreliability of structural system under non-stationary random excitations. Ascompared with the power spectrum method, the proposed method does notrequire a large amount of numerical integrals in both frequency and timedomains. Furthermore, the assumptions are no longer required in the presentapproach with respect to the probability distribution of the excursionnumber and the correlation between different failure modes. With numericalexamples, the calculation accuracy and efficiency of the proposed method arecompared with those of the conventional Monte Carlo simulation method, thePoisson process method and the Markov process method. Numerical resultsindicate that the proposed method has perfect accuracy and reasonably highefficiency.