Exact solutions of (2+1)-dimensional ZK-MEW equation are obtained with the improved simple equation method, including hyperbolic and trigonometric function solutions. When the special values of parameters in hyperbolic function solutions are given, the solitary wave solutions can be obtained. When the special values of parameters in trigonometric function solutions are given, the periodic wave solutions can be obtained. Practice shows that simple equation method has a wide range of applications in optoelectronics, quantum optics, laser physics and plasma physics fields.