In　this　paper,　an　efficient　method　is　proposed　for　constructing　the　seismic　fragility　curves　of　bridge　piers,　in　which　the　dynamical　reliability　assessment　is　developed　from　methods　of　moment.　The　main　procedure　for　constructing　seismic　fragility　curves　consists　of　four　steps.　First,　the　non-stationary　seismic　acceleration　process　samples　are　simulated　by　the　random　function-spectrum　representation　model　(RFSRM)　with　one　elementary　random　variable　at　a　given　PGA　value.　Second,　the　first　four　moments　(i.e.,　mean　value,　standard　deviation,　skewness　and　kurtosis)　of　extreme　structural　response　are　then　evaluated　from　the　extremum　of　each　nonlinear　time-history　seismic　response　based　on　RFSRM.　Third,　the　failure　probability　is　then　estimated　by　the　fourth-moment　reliability　index,　which　is　derived　from　an　explicit　fourth-moment　transformation.　Finally,　the　seismic　fragility　curves　can　be　constructed　by　repeating　the　three　steps　and　considering　different　PGA　values　and　damage　levels　(i.e.,　slight,　moderate,　extensive,　and　complete).　The　efficiency　and　accuracy　of　the　proposed　methodology　are　demonstrated　by　a　numerical　example　for　constructing　the　fragility　curves　of　a　high-speed　railway　bridge　pier　in　which　the　direct　incremental　dynamic　analysis　(IDA)　method　based　on　Monte　Carlo　simulations　are　employed　for　comparison.