We proposed a five-speed lattice Boltzmann method to investigate the evolutionof the reaction-diffusion system. As an example, the production mechanism and evolution of the spiral wave were studied. We found that the system may evolve to three final states: homogenous, chaotic, and spiral waves-like, depending on the parameter of the system, and the crushing of the spiral waves in Selkov reaction-diffusion system belongs to the Doppler class.