Based on the Priestley’s evolutionary spectral representation theory and the idea of random function, a hybrid spectral representation and random function approach is presented to simulate non-stationary stochastic processes. This approach uses two basic random variables to capture accurately the second-order statistics of the original stochastic process. Discrete representative points of two basic random variables are selected, and representative sample functions with assigned probability are generated directly by the evolutionary power spectral density function. By means of the evolutionary power spectral density function of non-stationary ground motion acceleration process, the effectiveness and advantages of this approach are demonstrated. Finally, combining the probability density evolution method, the random dynamic response and reliability of the Duffing oscillator subjected to stochastic ground motions are investigated.