For　time-variant　imprecise　reliability　problem　with　parameterized　probability-box　(p-box),　determining　the　upper　and　lower　bounds　of　time-variant　failure　probability　is　usually　more　of　concern　for　engineers.　To　compute　these　two　bounds,　this　paper　proposes　a　new　extreme　value　moment　method　(EVMM)　combining　adaptive　Kriging　model.　In　the　proposed　method,　the　adaptive　Kriging　models　are　first　employed　to　approximate　limit　state　function　(LSF)　responses　and　the　predicted　values　are　mapped　into　the　extreme　value　function　(EVF)　counterparts.　Then,　the　weighted　approach　based　on　sparse　grid　numerical　integration　(WA-SGNI)　is　developed　to　estimate　the　statistical　moments　of　the　approximated　EVF　responses.　The　resulting　moments　are　further　used　to　decouple　the　calculation　of　bounds　of　time-variant　failure　probability　into　two　deterministic　optimization　problems.　The　accuracy　and　efficiency　of　the　proposed　method　for　time-variant　imprecise　reliability　analysis　are　demonstrated　through　three　numerical　examples　with　LSFs　involving　non-Gaussian　processes　and　finite　element　analysis.