The　spatiotemporal　variability　exists　in　almost　all　engineering　problems,　since　the　environmental　actions　and　material　properties　may　change　both　spatially　and　temporally　in　a　stochastic　manner.　Therefore,　reliability　analysis　is　inherently　space-time-dependent.　In　this　study,　an　innovative　space-time-dependent　outcrossing　rate　(STOR)　method　is　proposed　for　dealing　with　such　reliability　problems.　The　failure　probability　of　a　structure　is　determined　based　on　outcrossing　rate　which　is　theoretically　derived　for　the　first　time,　considering　the　spatio-temporal　variability　of　all　basic　variables.　Then,　an　efficient　numerical　algorithm　for　computing　the　failure　probability　is　proposed　based　on　Gauss-Legendre　quadrature.　The　application　of　STOR　method　is　investigated　through　three　examples,　including　non-Gaussian　random　processes,　non-Gaussian　random　fields,　strong　nonlinear　limit　state　functions　and　small　failure　probability　problems.　The　proposed　STOR　method　is　found　to　be　efficient　for　space-time-dependent　reliability　analysis　with　enough　accuracy.