In　recent　decades,　the　outcrossing　rate　method　has　gained　popularity　for　structural　time-dependent　reliability　assessments　(TRA).　Despite　numerous　efforts,　developing　a　general　analytical　outcrossing　rate　method　for　a　nonstationary　non-Gaussian　performance　function　to　estimate　the　failure　probability　within　the　forecast　time　interval　remains　a　significant　challenge.　This　paper　introduces　an　analytical　outcrossing　rate　method　for　non-Gaussian　cases,　named　the　three-moments-based　outcrossing　rate　(TMO)　method.　The　outcrossing　rate　is　formulated　based　on　the　third-moment　outcrossing　rate　with　no　assumption　of　the　correlation　between　the　performance　function　and　its　derivative　process,　allowing　for　a　comprehensive　understanding　of　the　performance　characteristics　of　a　structure.　Following　the　development　of　the　proposed　outcrossing　rate,　a　TRA　methodology　is　established　to　evaluate　the　failure　probability　of　the　nonstationary　non-Gaussian　performance　function.　Notably,　the　TMO　method　only　requires　statistical　moments　of　the　nonstationary　non-Gaussian　performance　function,　which　are　easy　to　calculate,　facilitating　efficient　implementation.　Three　numerical　examples　are　presented　to　demonstrate　the　applicability,　efficiency,　and　accuracy　of　the　proposed　TMO　method.　It　can　be　concluded　that　the　proposed　TMO　method　provides　an　accurate　and　useful　approach　for　TRA　in　engineering　applications.