There is the widespread existence of wave phenomena in physics, chemistry and biology [1, 2].This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved.In this talk, we present a nonlinear reaction-diffusion system, which can be considered as a generalization of the Fisher equation.Applying the qualitative theory of planar dynamical systems, we show that under certain conditions, the nontrivial bounded traveling wave solution for the system is monotone or oscillatory.We then present a class of traveling wave solutions to the nonlinear reaction-diffusion system by using the Cole-Hopf transformation and the Lie symmetry method.