Abstract: A kind of mathematical model for chemical reactions of grain brewing with saturated reaction rate is analyzed. By using qualitative analytical methods of ordinary differential equations, the behaviour of equilibrium point, uniform boundedness of the solution, global asymptotic stability of the positive equilibrium of the system are discussed, and the conditions under which there is not limit cycles are obtained. The theoretical results show that if the parameters satisfy some conditions, then the process of brewing wine can be sustainable and steady.