Using the extended G/G′ expansion method, the twenty group of exact solutions for ZS equation were constructed. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with arbitrary parameters to the equation were obtained. When the arbitrary parameters in hyperbolic function solutions are taken as some special values, the solitary wave solutions can be obtained by analyzing the properties of solutions. When the arbitrary parameters in trigonometric function solutions are taken as some special values, the trigonometric function solutions can be expressed as periodic wave solutions. Some new exact solutions can be obtained by applications of improved G/G' expansion method with larger scope of the solutions.