In　this　paper,　we　mainly　investigate　the　weak　convergence　analysis　about　the　error　terms　which　are　determined　by　the　discretization　for　solving　the　stochastic　differential　equation　(SDE,　for　short)　in　forward-backward　stochastic　differential　equations　(FBSDEs,　for　short),　which　is　on　the　basis　of　Ito　Taylor　expansion,　the　numerical　SDE　theory,　and　numerical　FBSDEs　theory.　Under　the　weak　convergence　analysis　of　FBSDEs,　we　further　establish　better　error　estimates　of　recent　numerical　schemes　for　solving　FBSDEs.