Recovering　the　probability　distribution　of　the　limit　state　function　is　an　effective　method　of　structural　reliability　analysis,　in　which　it　still　is　challenging　to　balance　the　precision　and　computational　efforts.　This　paper　proposes　an　adaptive　mixture　of　normal-inverse　Gaussian　distributions　which　exhibits　high　flexibility　to　deal　with　this　issue.　First,　the　mixture　distributions　with　two　components　were　revisited　briefly,　and　the　limitations　are　pointed　out.　Then　the　proposed　mixture　distribution　was　established.　According　to　the　limit　condition,　one　or　two　components　are　employed　in　the　proposed　mixture　distribution　to　represent　the　unknown　distribution　of　the　limit　state　function　(LSF),　which　makes　the　mixture　distribution　adaptive.　To　specify　the　unknown　parameters　effectively,　the　Laplace　transform　at　some　discrete　values　is　utilized,　in　which　a　set　of　nonlinear　equations　can　be　solved　easily.　An　effective　cubature　rule　is　utilized　to　assess　numerically　the　Laplace　transform　and　the　involved　moments,　which　can　guarantee　the　efficiency　and　precision　for　structural　reliability　computation.　After　the　LSF＇s　distribution　is　attained,　the　failure　probability　can　be　evaluated　readily　via　an　integral　over　the　distribution.　Five　numerical　examples　were　provided　to　indicate　the　result　of　the　proposed　method.