We investigated the dynamics of the simple spiral waves of the Selkov reaction-diffusion system with the Lattice Boltzmann method. The results of computer simulation lead to the conclusion that the trajectory of the spiral tip is a small circle, the wavelength and the period decay exponentially when the value of parameter b increases; and the relation between the wavelength and the period is λ∝T^1/2, which is qualitatively the same as that obtained by Ou-Yang Qi from Belousov-Zhabotinsky reaction system.