Abstract: On the basis of Priestley’s evolutionary spectral representation theory, this paper presents a spectral representation for simulation of non-stationary stochastic processes. Following this method, sample processes can be generated using a cosine series formula. It is shown that, these sample processes accurately reflect the prescribed probabilistic characteristics of the stochastic process when the number of the terms in the cosine series is large; and the ensemble expected value and the ensemble autocorrelation function approach the corresponding target functions, respectively, as the sample size increases; and these sample processes are asymptotically normal as the number of the terms in the series tends to infinity. The most prominent feature of this method is that expected sample processes may be generated by certain random phase angles.