With　the　rapid　development　of　energy-based　seismic　design,　probabilistic　seismic　hazard　analysis　(PSHA)　in　terms　of　the　input　energy　spectrum,　E　I,　has　become　increasingly　important.　Generally,　implementing　E　I-based　PSHA　requires　a　ground-motion　prediction　equation　(GMPE)　for　E　I.　However,　although　a　GMPE　for　E　I　can　be　constructed　in　regions　with　abundant　earthquake　data　based　on　regression　analyses,　it　is　difficult　to　obtain　in　regions　lacking　strong　ground-motion　records.　Therefore,　this　study　proposes　a　new　approach　for　performing　E　I-based　PSHA　in　regions　with　limited　earthquake　data.　Instead　of　using　a　GMPE　for　E　I　directly,　a　model　of　Fourier　amplitude　spectrum　(FAS)　is　adopted,　which　can　be　determined　using　a　small　number　of　earthquake　data　with　small-to-moderate　magnitudes.　Then,　the　E　I　of　the　ground　motion　is　obtained　from　FAS　based　on　the　relationship　between　E　I　and　FAS.　Furthermore,　to　calculate　the　annual　intensity　exceedance　rate　within　the　proposed　framework　of　adopting　the　FAS　model,　a　highly　efficient　method,　namely,　the　moment　method,　is　applied.　Several　numerical　examples　indicate　that　the　proposed　approach　not　only　is　suitable　for　regions　lacking　strong　ground-motion　records　but　also　performs　very　efficiently　in　calculating　the　annual　intensity　exceedance　rate.　©　The　Author(s)　2024.