A　method　for　calculating　the　first　four　moments　of　structural　extremum　responses　is　proposed　based　on　the　random　function-spectral　representation　model.　A　high-order　moment　method　for　structural　dynamic　reliability　analysis　under　non-Gaussian　random　excitation　is　developed.　The　discrete　point　set　expression　of　a　single　basic　random　variable　of　a　random　function　is　modified.　A　small　amount　of　non-Gaussian　acceleration　processes　is　generated　according　to　the　modified　discrete　point　set,　and　the　time　history　analysis　of　the　structure　is　performed,　then　the　first　four　moments　(i.e.,　mean,　standard　deviation,　skewness　and　kurtosis)　of　non-Gaussian　structural　extreme　responses　are　estimated.　The　complete　expression　of　the　fourth-order　moment　reliability　index　is　proposed　and　applied　to　calculate　the　structural　dynamic　reliability　under　non-Gaussian　random　excitation.　Finally,　the　accuracy　and　efficiency　of　the　proposed　method　are　demonstrated　by　the　dynamic　reliability　analysis　of　a　two-degree-of-freedom　system　and　an　eight-story　frame　structure.　Although　the　number　of　samples　is　significantly　reduced,　the　maximum　relative　error　of　the　first　four　moments　calculated　by　the　proposed　method　is　5.54%　compared　with　the　Monte　Carlo　simulation　results.　The　results　of　dynamic　reliability　analysis　by　the　proposed　method　are　almost　the　same　with　those　of　Monte　Carlo　simulation.　©　2020,　Nanjing　Univ.　of　Aeronautics　an　Astronautics.　All　right　reserved.