In　order　to　study　aseismic　reliability　of　bridge　piers　under　their　non-linear　seismic　responses,　the　random　function-spectrum　representation　model　and　high-order　moment　method　were　introduced　to　propose　a　bridge　pier＇s　aseismic　reliability　analysis　approach　based　on　first　four　moments　of　extreme　structural　responses.　Firstly,　a　three-line　restoring　force　model　was　considered　to　establish　a　single　column　model　of　bridge　pier.　Secondly,　the　random　function-spectrum　representation　model　was　used　to　generate　non-stationary　seismic　acceleration　time-history　samples,　and　non-linear　time　history　analysis　was　conducted　for　the　bridge　pier＇s　structural　responses.　Then,　the　calculation　framework　for　first　four　moments　including　mean,　standard　deviation,　skewness　and　kurtosis　of　extreme　structural　responses　was　established.　Finally,　the　pier　displacement　limit　was　considered　to　deduce　the　pier　displacement＇s　performance　function,　and　the　high-order　moment　method　was　used　to　calculate　the　bridge　pier＇s　aseismic　reliability　index.　Through　the　bridge　pier＇s　structural　analysis,　the　effectiveness　and　precision　of　the　proposed　method　were　verified.　The　results　showed　that　compared　with　the　simulation　results　using　Monte　Carlo　method,　the　maximum　relative　errors　of　first　four　moments,　aseismic　reliability　index　and　failure　probability　calculated　using　the　proposed　method　are　0.28%,　1.92%　and　4.92%,　respectively;　the　proposed　method　provides　an　effective　way　for　evaluating　aseismic　reliability　of　bridge　piers.　©　2020,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.