In this paper，we have studied the nonlinear waves using the Greenberg-Hasting Cellular Automaton model. The dependence of the propagation speed of plane wave on the neighbor radius and the excitation threshold is analyzed with the no-flux boundary condition by computer simulation, and then the excitation condition is obtained. The orbit of the tip of spiral wave is affected by the number of refractory states and the excitation threshold, and then the mechanism is analyzed.