In　this　paper,　we　propose　an　energy-conservative　finite　difference　time　domain　(FDTD)　method　for　solving　the　coupled　nonlinear　Klein-Gordon　equations　(CNKGEs)　in　the　nonrelativistic　limit　regime,　involving　a　small　parameter　0　＜　epsilon　＜＜　1　which　is　inversely　proportional　to　the　speed　of　light.　Employing　cut-off　technique,　we　analyze　rigourously　error　estimates　for　the　numerical　method.　Numerical　results　are　reported　to　confirm　the　energy-conservative　property　and　the　error　results　in　l(2)　norm　and　H-1　norm　under　different　values　of　epsilon.