Abstract: in order to simulate the energy distribution in low frequency region of the earthquake ground motion better by the models of power spectral density,and taking into account the simplicity and usability at the same time,two types of modified power spectral density (PSD) models are presented in this study: modified Kanai-Tajimi model and modified Hu-Zhou model.The stochastic response of the single degree of freedom structure disturbed by the stationary stochastic process with the frequency characters represented by above two PSD models are deducted;According to the stochastic response of single degree-of-freedom structure subjected to stationary random processes,six kinds of PSD models have been compared. The investigations shows that the modified Hu-Zhou model can reasonably represent the energy distribution of seismic ground motion in frequency domain,the earthquake response of structure excited by modified Hu-Zhou model consistent with the typical real acceleration records.The modified Kanai-Tajimi model make up the low-frequency-default of kanai-Tajimi model to some extent,and then can be used as its replacement.