Time-dependent　system　reliability　analysis　still　faces　severe　challenges　including　the　simultaneous　consideration　of　time-dependent　uncertainties　under　multiple　failure　modes　and　the　accurate　estimation　of　small　failure　probability.　Therefore,　this　paper　proposes　a　nested　single-loop　Kriging　(NSLK)　model　coupled　with　subset　simulation　(SS)　method,　named　NSLK-co-SS,　for　time-dependent　system　reliability　assessment.　Firstly,　based　on　the　rationale　of　SS　method,　the　small　time-dependent　system　failure　probability　is　converted　into　the　product　of　a　series　of　large　intermediate　failure　probabilities　by　introducing　a　series　of　intermediate　failure　events.　Then,　by　reformulating　the　time-dependent　system　reliability　problem　as　a　nested　system　reliability　one,　the　NSLK　method　is　developed　to　estimate　each　intermediate　failure　probability.　Meanwhile,　a　system　reliability　theory-based　U　(SYSU)　learning　function　is　proposed　to　identify　both　the　best　training　sample　and　mode　and　sequentially　update　the　Kriging　models　of　multiple　modes　in　a　series　of　small　intermediate　sample　pools.　Two　numerical　examples　and　an　engineering　example　were　investigated　to　demonstrate　the　efficiency　and　accuracy　of　the　proposed　method.