Abstract: Using the（g^'/g^2）-expansion method,exact solutions for coupled nonlinear Klein-Gordon equation are constructed. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with arbitrary parameters to the equations are obtained. When the arbitrary parameters in hyperbolic function solutions are taken as special values, the solitary wave solutions can be obtained. By introducing a parameter, the trigonometric function solutions can be expressed as periodic wave solutions.