The　high-order　moment　methods,　being　very　simple,　are　widely　used　for　structural　reliability　analysis.　The　basic　procedure　of　moment　methods　includes　two　steps:　firstly,　the　first　few　moments　of　the　performance　function　were　determined　using　the　new　point　estimate　method;　secondly,　the　corresponding　failure　probability　can　be　obtained　from　the　moment-based　reliability　index.　In　the　new　point　estimate　method,　the　basic　random　variables　are　assumed　having　known　probability　distributions　to　realize　the　Rosenblatt　transformation　and　its　inverse　transformation.　However,　in　practical　applications,　the　probability　distributions　of　some　random　variables　maybe　unknown,　and　the　probabilistic　characteristics　of　these　variables　maybe　expressed　using　only　statistical　moments.　This　paper　aims　to　investigate　the　high-order　moment　methods　including　random　variables　with　unknown　probability　distribution　based　on　the　fourth-moment　transformation　technique.　Several　examples　are　examined　under　different　conditions　to　demonstrate　the　accuracy　and　efficiency　of　the　present　method.　Since　only　the　first　few　moments　of　the　performance　functions　are　used,　and　it　can　be　conducted　even　when　the　probability　distributions　of　the　random　variables　are　unknown,　structural　reliability　analysis　should　become　simpler　and　more　convenient　using　the　present　method.　©　13th　International　Conference　on　Applications　of　Statistics　and　Probability　in　Civil　Engineering,　ICASP　2019.　All　rights　reserved.