A　new　time-frequency　modulating　function　with　a　novel　equivalent　average-intensity　envelope　based　on　the　instantaneous　energy　is　proposed　to　simulate　fully　nonstationary　ground　motions.　The　new　model　utilizes　simple,　uncoupled,　and　statistically　well-studied　temporal　and　spectral　nonstationary　parameters.　Then,　a　period-by-period　simulation　method　based　on　the　proposed　stochastic　model　is　developed　to　match　multiple　targets.　A　numerical　comparison　shows　that　the　new　method　replicates　well　both　the　target　temporal　and　spectral　nonstationarities　and　it　is　efficient　and　easy　to　use　in　engineering　practice.　This　study　also　demonstrates　that　for　obtaining　site-specific　seismic　input　by　means　of　site　response　analysis:　(1)　the　frequency　contents　of　bedrock　motion,　including　the　energy　concentration　in　terms　of　frequency　and　frequency　decaying　with　respect　to　time,　have　a　significant　impact　on　the　site　response　with　moderate　and　large　PGA　levels;　(2)　using　the　proposed　instantaneous-frequency-related　time　modulating　function　to　approximate　the　real　ground　motion　leads　to　results　sufficiently　close　to　the　record　for　nonlinear　site　response　regardless　PGA　levels　and　site　condition.　Therefore,　attention　should　be　paid　to　the　change　of　nonstationary　characteristics　of　ground-motion　frequency　according　to　the　source,　path,　and　site　condition　when　simulating　ground　motion　on　bedrock.　As　the　proposed　methods　can　approximately　control　various　ground-motion　characters,　different　targets　of　ground-motion　simulation　can　be　matched　for　different　engineering　purpose　such　as　site　response　analysis,　time-history　analysis　of　special　structures,　etc.　©　2021　John　Wiley　&　Sons　Ltd.