Abstract: To study the chemical waves in a double-molecule reaction-diffusion system coupled with the quadratic decay reaction, the theoretical analysls method and the numerical calculation were used. The theoretical model of this kind of reaction-diffusion system was established. The essential condition of the chemical waves occuring and the minimum speed of the chemical waves were derived by the kinetics analysis. The curves of the concentration dlstrlbution of the reactant and the catalyst were simulated with difference parameters. The theoretical model set up in this paper can generates the chemical waves.