Outcrossing　method　has　been　widely　applied　in　time-dependent　reliability　analysis　(TRA),　where　the　cumulative　failure　probability　is　calculated　based　on　the　numerical　integration　of　outcrossing　rate.　The　efficiency　of　out　crossing　method　is　influenced　by　two　factors,　i.e.,　the　number　of　discretized　instants　for　numerical　integration　and　the　computational　time　for　solving　outcrossing　rate　at　each　instant.　Focusing　on　these　factors,　an　efficient　Gauss-Legendre　quadrature　based　outcrossing　(GLO)　method　is　proposed　in　this　study.　The　main　innovation　of　the　proposed　method　consists　of　two　aspects.　First,　the　cumulative　failure　probability　is　evaluated　by　weighted　sum　of　outcrossing　rate　at　only　three　to　five　instants　with　the　aid　of　Gauss-Legendre　quadrature,　which　avoids　the　time-consuming　numerical　integration　with　a　large　number　of　instants　discretized.　Second,　an　efficient　algorithm　for　computing　outcrossing　rate　is　developed　from　a　recently　proposed　system　reliability　method　based　on　the　well-known　FORM/SORM.　Three　examples　are　presented　to　demonstrate　the　application　of　the　proposed　GLO　method,　including　explicit,　implicit,　and　strong　nonlinear　limit　state　functions.　It　is　shown　that,　reliability　results　by　the　proposed　GLO　method　are　in　close　agreement　with　those　by　Monte　Carlo　simulation,　with　the　computational　time　significantly　reduced.