The main goal of this paper is to study the asymptotic behavior of a coupled Klein-Gordon-Schr¨odinger system in three dimensional unbounded domain. We prove the existence of a global attractor of the systems of the nonlinear Klein-Gordon-Schr¨odinger (KGS) equations in H1(R3) × H1(R3) ×L2(R3) and more particularly that this attractor is in fact a compact set of H^2(R^3) × H^2(R^3) × H1(R^3).