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.