In　practice,　structural　limit　state　function　(LSF)　is　often　combined　with　finite　element　(FE)　models,　and　the　corresponding　time-dependent　reliability　assessment　(TRA)　inevitably　involves　dealing　with　computational　inefficiency.　In　this　paper,　a　general　moment-based　outcrossing　rate　(GMO)　method　is　proposed　to　conduct　TRA　efficiently,　with　no　limitation　in　the　form　of　LSF.　There　are　two　innovations　of　GMO　method:　firstly,　an　explicit　moment-based　outcrossing　rate　is　developed;　secondly,　a　separate　algorithm　is　proposed　that　facilitates　the　separation　of　FE　analysis　from　TRA　cycle.　The　proposed　method　minimizes　the　computational　cost　associated　with　FE　analysis　and　enables　TRA　cycle　to　be　conducted　more　efficiently　with　the　assistance　of　an　explicit　moment-based　outcrossing　rate　and　explicit　moment-based　outcrossing　rate.　Three　numerical　examples　are　investigated　to　examine　the　accuracy　and　efficiency　of　GMO　method　for　TRA　cycle.　GMO　method　is　found　from　the　results　that　it　can　efficient　and　accurate　to　conduct　TRA.　Such　improvements　in　computational　efficiency　are　particularly　valuable　for　complex　structures　where　FE　analysis　is　computationally　expensive　and　time-consuming.