In　this　paper,　Gauss-legendre　integral　formulation　and　Gauss-legendre　integral　points　estimation　method　are　proposed　to　solve　the　reliability　of　stochastic　structure　under　seismic　excitation,　based　on　the　first-passage　method　modified　by　Vanmarcke.　Numerical　simulation　shows　that　Gauss-legendre　integral　method　is　only　suitable　for　system　whose　dimension　is　less　than　4,　offering　great　precision　and　higher　computational　efficiency.　By　contrast,　Gauss-legendre　integral　points　estimate　method　possesses　excellent　precision　and　much　higher　computational　efficiency.　Both　the　mean　and　variation　coefficient　of　structural　reliability　solved　by　those　two　methods　are　converged　with　increase　in　variability　coefficient　of　structure　parameters.　©,　2015,　Nanjing　University　of　Aeronautics　an　Astronautics.　All　right　reserved.