In　this　paper,　we　prove　finite-time　blowup　in　energy　space　for　the　three-dimensional　Klein-Gordon-Zakharov　(KGZ)　system　by　modified　concavity　method.　We　obtain　the　blow-up　rates　of　solutions　in　local　and　global　space,　respectively.　In　addition,　by　using　the　energy　convergence,　we　study　the　subsonic　limit　of　the　Cauchy　problem　for　KGZ　system　and　prove　that　any　finite　energy　solution　converges　to　the　corresponding　solution　of　Klein-Gordon　equation　in　energy　space.