Network　connectivity　reliability　is　imperative　to　lifeline　systems,　such　as　water　distribution　systems,　and　transportation　networks.　However,　the　computation　of　network　connectivity　reliability　is　highly　complicated　due　to　the　large　number　of　binary-stated　network　components,　the　diversity　of　post-hazard　network　topologies,　and　the　correlation　among　network　component　failures.　This　paper　presents　an　efficient　method,　integrated　with　Monte　Carlo　simulation　(MCS),　for　computing　network　connectivity　reliability　specifically　for　binary-stated　component　networks,　taking　into　account　failure　correlations.　In　particular,　a　concise　transformation　method　for　correlated　discrete　Bernoulli　distribution　is　developed,　enabling　the　capture　of　critical　safe-failed　states　of　network　components　as　well　as　the　conversion　into　independent　standard　normal　space.　The　proposed　method　is　then　combined　with　an　efficient　shortest　path　search　method　to　determine　whether　the　network　is　connected　or　not,　facilitating　the　computation　of　connectivity　reliability　for　large-scale　and　dense　networks.　The　results　of　examples　show　that　the　proposed　method　is　more　accurate　and　efficient　than　existing　methods,　and　it　can　also　obtain　the　influence　range　of　component　failure　correlation　on　connectivity　reliability.　For　disaster　response　and　management　of　large,　dense　lifeline　networks,　the　proposed　method　has　significant　advantages　in　providing　fast　and　accurate　assessments.