In　order　to　investigate　the　frequency-domain　characteristic　of　reliability　and　the　damping　performance　of　a　tuned　mass　damper　(TMD)　system,　the　probability　distribution　formula　about　the　spectral　moment　of　cut-off　frequency　of　a　structure　under　random　excitations　is　derived　based　on　the　first-passage　failure　criterion,　and　the　frequency-domain　probability　density　is　solved　using　the　forward　difference　scheme.　Then,　the　frequency-domain　probability　information　of　the　TMD　system　is　also　analyzed　by　the　above　method.　The　results　show　that　the　frequency-domain　probability　density　is　negative,　and　the　frequency-domain　probability　tends　to　the　value　calculated　by　the　first-passage　failure　criterion　as　the　frequency　band　increases.　For　a　structure　without　control,　the　percentage　of　the　reliability　reduction　at　the　first　two　mode　frequencies　are　59.23%　and　35.45%,　respectively,　while　counterparts　of　the　TMD　system　are　34.54%　and　55.92%.　The　frequency-domain　reliability　analysis　reveals　that　the　TMD　system　has　a　reliable　damping　effect,　mainly　by　controlling　the　first　mode　vibration　of　the　structure.　©,　2015,　Science　Press.　All　right　reserved.