The Zeldovich-von Neumann-Doring model and the Chapman-Jouguet model for a simplified combustion model--Majda’s model is studied. The author proves a uniform maximum norm estimate, then proves that as the rate of chemical reaction tends to infinity the solutions to the Zeldovich-von Neumann-Doring model tend to that of the Chapman-Jouguet model. The type of combustion waves is studied. This result is compared with the result of the projection and finite difference method for the same model.