Global　synchronization　analysis　for　complex　networks　with　coupling　delay　is　investigated.　Firstly　the　constant　time　delay　is　analyzed　and　then　the　case　for　time-varying　delay　is　considered.　Sufficient　conditions　for　network　synchronization　are　given　based　on　Lyapunov　functional,　linear　matrix　inequality,　and　Kronecker　product　technique.　The　unknown　variables　in　the　sufficient　conditions　are　fewer　than　those　in　the　recent　reference.　Moreover,　for　the　time-varying　delay　case,　we　find　that　the　conditions　are　dependent　on　the　bounds　of　both　time　delay　and　its　derivative,　and　the　derivative　of　the　time-varying　delay　can　be　any　value　in　the　bounds.　Finally,　numerical　examples　are　given　to　validate　the　effectiveness　of　the　obtained　results.