This　paper　addresses　the　first　passage　problem　of　linear　systems　subjected　to　non-Gaussian　excitations　by　means　of　simulation.　A　non-Gaussian　simulation　technique　based　on　the　unified　Hermite　polynomial　model　(UHPM)　is　adopted　to　model　input　excitations,　and　then　the　output　responses　are　further　obtained　through　time-domain　analysis.　The　novel　contribution　of　this　paper　is　to　construct　an　efficient　importance　sampling　(IS)　density　function　based　on　UHPM　and　the　first-order　reliability　method　(FORM)　to　release　the　computational　burden.　A　simple　and　efficient　sampling　procedure　is　also　provided　for　convenient　implementation.　Such　an　approach　allows　the　failure　probabilities　in　the　order　of　10-3　or　lower　to　be　estimated　reliably　with　a　reduced　computational　cost.　The　accuracy　and　efficiency　of　the　proposed　method　are　demonstrated　by　three　examples,　including　a　single-degree-of-freedom　oscillator,　a　3-story　linear　shear　frame,　and　a　relatively　large-scale　finite-element　model.　(C)　2021　American　Society　of　Civil　Engineers.