Bayesian　updating　of　the　reliability　of　deteriorating　engineering　structures　based　on　inspection　data　has　been　attracting　a　lot　of　attention　recently　because　it　can　provide　more　accurate　estimates　of　the　structural　reliability　as　the　number　of　inspection　data　increases.　However,　in　the　process　of　updating　the　reliability　of　deteriorating　structures,　it　is　not　a　trivial　work　to　obtain　the　posterior　distribution　of　the　random　variable　of　interest　due　to　its　multidimensional　parameter　integral　space　and　complex　integral　function.　This　paper　presents　a　new　effective　method　for　obtaining　the　explicit　posterior　distribution　for　the　random　variable　of　interest　and　evaluating　time-variant　reliability　combined　with　all　updated　random　variables.　In　the　proposed　method,　the　Smolyak-type　quadrature　formula　is　first　applied　to　obtain　the　first　three　posterior　moments　of　the　uncertain　parameters,　and　the　three-parameter　lognormal　distribution　is　used　to　approximate　their　posterior　probability　distributions.　Then,　the　two-layer　Smolyak-type　sparse　grid　is　adopted　to　estimate　the　first　three　posterior　moments　of　the　random　variable　of　interest,　and　its　explicit　posterior　distribution　can　also　be　approximated　by　the　three-parameter　lognormal　distribution.　Finally,　the　time-variant　reliability　analysis　considering　Bayesian　updating　is　conducted　using　all　updated　random　variables.　Numerical　examples　demonstrate　that　the　proposed　method　requires　less　computational　cost,　but　the　results　provided　are　almost　the　same　as　those　of　the　Markov　chain　Monte　Carlo　simulation.　(c)　2021　American　Society　of　Civil　Engineers.