Time-variant　reliability　analysis　(TRA)　has　drawn　tremendous　interest　of　engineers　attributable　to　its　ability　in　assessing　the　probability　that　a　system　performs　its　intended　function　over　the　time　interval　of　interest.　This　paper　proposes　a　new　simulation　method　for　TRA　by　combining　moment-based　Hermite　polynomial　model　(HPM)　and　importance　sampling　(IS).　By　evaluating　the　statistical　moments　of　limit　state　function　(LSF)　and　using　moment-based　HPM,　the　LSF　is　transformed　into　a　moment-based　equivalent　Gaussian　process.　Then,　based　on　the　concept　of　the　composite　limit　state,　the　time-variant　reliability　problem　is　equivalent　to　solving　a　multi-dimensional　Gaussian　integral.　To　improve　the　computational　efficiency,　an　efficient　updating　strategy　is　proposed　to　simultaneously　construct　Kriging　models　for　both　the　mean　value　function　and　auto-correlation　function　of　this　process.　Meanwhile,　an　efficient　IS　method　is　also　developed　to　combine　Expansion　Optimal　Linear　Estimation　for　solving　multi-dimensional　Gaussian　integral.　The　efficiency　and　accuracy　of　the　proposed　method　is　demonstrated　through　three　numerical　examples　involving　nonlinear　LSFs　and　non-stationary　non-Gaussian　processes.