In　this　paper　we　study　the　well　posedness　of　solution　to　a　certain　system　of　nonlinear　Klein-Gordon-Schroumldinger　equations　in　three　space　dimensions.　Basing　on　the　Strichartz　estimates,　we　obtain　the　global　existence,　uniqueness　of　the　solutions,　and　continuous　dependence　with　respect　to　initial　data　in　the　Sobolev　spaces　of　low　regularities　by　setting　appropriate　contraction　and　taking　difference　estimates.