In this talk, we consider the Cauchy problem of a model for the one-dimensional viscous radiative and reactive gas. For such a specific gas motion, a somewhat surprising fact is that, unlike the ideal gas, the pressure is not a convex function of the specific volume and the specific entropy. We first show that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant and the strength of the rarefaction waves are sufficiently small. Then we deal with the case when the viscosity depends on both density and the absolute temperature.