In　this　paper,　we　consider　the　energy　conserving　numerical　scheme　for　cou-pled　nonlinear　Klein-Gordon　equations.　We　propose　energy　conserving　finite　element　method　and　get　the　unconditional　superconvergence　result　O(h2+Delta　t2)　by　using　the　er-ror　splitting　technique　and　postprocessing　interpolation.　Numerical　experiments　are　carried　out　to　support　our　theoretical　results.