Structural　reliability　assessment　is　of　great　significance　for　the　safety　and　maintenance　of　structures.　In　recent　years,　the　moment　method　has　been　rapidly　developed　and　applied　widespread　for　its　simplicity　and　performance.　Sometimes,　the　accuracy　of　the　moment　method,　using　only　the　first　four　moments　(i.e.,　mean　value,　standard　deviation,　skewness,　and　kurtosis),　is　not　sufficient　in　evaluating　the　reliability　index　of　strong　non-Gaussian　performance　functions.　In　this　study,　a　method　based　on　the　quartic　normal　transformation　(QNT)　is　proposed　for　structural　reliability　assessment,　which　enables　incorporation　of　the　first　five　moments,　including　the　super-skewness,　of　performance　function.　The　structural　reliability　index　based　on　the　QNT　model　is　derived.　The　first　five　moments　of　the　performance　function　are　estimated　by　introducing　the　point　estimate　method.　Seven　engineering　examples　are　employed　to　demonstrate　the　efficacy　of　the　QNT.　The　results　show　that　the　computational　efficiencies　of　CNT　and　QNT　were　close　to　each　other　and　both　superior　to　that　of　MCS.　The　results　also　show　that　the　performance　of　QNT　is　superior　to　CNT　in　aspect　of　accuracy　and　robustness　in　particular　to　performance　functions　with　strong　non-Gaussianity.