In　practical　engineering,　it　is　usually　necessary　to　compute　the　small　first-passage　probability　of　dynamic　systems　exposed　to　nonstationary　stochastic　excitations.　However,　it　is　still　a　challenging　problem　to　efficiently　estimate　the　super-small　failure　probability　using　an　approximate　extreme　value　distribution　(EVD)　based　on　a　small　number　of　simulated　samples.　In　this　study,　a　novel　EVD　model　is　proposed　to　describe　the　probability　distribution　of　the　structural　extreme　response　induced　by　nonstationary　stochastic　excitations.　This　EVD　model　consists　of　two　parts:　the　main　body　is　modeled　by　a　truncated-shifted　generalized　lognormal　distribution,　and　a　monotonic　exponential　model　is　proposed　to　fit　the　tail　region.　Besides　that,　a　criterion　for　determining　the　breakpoint　between　the　main　body　and　tail　region　is　proposed,　which　ensures　the　non-negativity　and　normativity　of　the　proposed　EVD　model　and　allows　the　EVD　to　be　reconstructed　accurately　and　efficiently,　particularly　in　its　tail　region.　In　this　regard,　the　corresponding　first　passage　probabilities　under　different　thresholds　can　be　straightly　evaluated.　The　precision　and　completeness　of　the　proposed　EVD　model　are　investigated　using　two　numerical　examples　that　consider　linear　and　nonlinear　frame　structures　subjected　to　nonstationary　ground　motion　accelerations.　The　results　show　that　the　proposed　model　is　in　excellent　agreement　with　the　results　of　Monte　Carlo　simulation,　even　when　the　failure　probability　is　very　small.　©　2023　Elsevier　Ltd