In this paper, we describe a method for solving the existence of traveling waves in a class of reaction-diffusion system whose propagating behavior of waves is similar to that in the KPP system. We will outline the method step by step. For each step, we use the quadratic autocatalytic reaction with a decay step to illustrate the method. This method might be applied to a class of prey-predator systems which do not enjoy the comparison principle. Further, the propagating phenomenon can be characterized in the sense of Aronson-Weinberger formulation.