With　the　rapid　development　of　energy-based　seismic　design,　probabilistic　seismic　hazard　analysis　(PSHA)　in　terms　of　the　input　energy　spectrum,　EI,　has　become　increasingly　important.　Generally,　implementing　EI-based　PSHA　requires　a　ground-motion　prediction　equation　(GMPE)　for　EI.　However,　although　a　GMPE　for　EI　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　EI-based　PSHA　in　regions　with　limited　earthquake　data.　Instead　of　using　a　GMPE　for　EI　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　EI　of　the　ground　motion　is　obtained　from　FAS　based　on　the　relationship　between　EI　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.