Information　on　the　distribution　of　the　basic　random　variable　is　essential　for　the　accurate　analysis　of　structural　reliability.　The　usual　method　for　determining　the　distributions　is　to　fit　a　candidate　distribution　to　the　histogram　of　available　statistical　data　of　the　variable.　Generally,　such　candidate　distribution　would　have　parameters　that　may　be　evaluated　from　the　statistical　moments　of　the　statistical　data.　Probability　distributions　are　usually　determined　using　one　or　two　parameters　evaluated　from　the　mean　and　standard　deviation　of　statistical　data.　However,　these　distributions　are　not　flexible　enough　to　represent　the　skewness　and　the　kurtosis　of　statistical　data.　Normal　transformation　is　often　used　in　probabilistic　analysis　especially　when　multivariate　non-normal　random　variables　are　involved.　This　study　proposes　a　probability　distribution　based　on　polynomial　normal　transform,　of　which　parameters　are　determined　using　the　first　four　L-moments　(L-mean,　L-standard　deviation,　L-skewness　and　L-kurtosis)　of　the　available　data.　The　simplicity,　generality,　flexibility　and　advantages　of　this　distribution　in　statistical　data　analysis　are　discussed.　The　results　are　found　to　better　than　two-　and　three-parameter　distributions,　and　similar　to　cubic　normal　distribution　based　on　central　moments　(C-moments).　With　the　aiming　at　illustrate　the　stability　of　polynomial　normal　transform　based　on　L-moments,　several　extreme　values　are　added　to　data.　The　proposed　distribution　is　demonstrated　to　provide　significant　stability　and　flexibility.　Then　this　method　is　applied　to　reliability　index　calculation,　and　its　significance　in　structural　reliability　evaluation　is　discussed.　The　calculation　results　are　compared　with　Monte　Carlo　calculations.　Several　numerical　examples　are　further　presented　to　demonstrate　the　accuracy　and　efficacy　of　the　distribution　for　conducting　reliability　analyses.　©　13th　International　Conference　on　Applications　of　Statistics　and　Probability　in　Civil　Engineering,　ICASP　2019.　All　rights　reserved.