  We propose the deterministic rate equation of three-species in the reaction -
diffusion system. For this case, our purpose is to carry out the decay process
in our three-species reaction-diffusion model of the form $A+B+C\to D$. The
particle density and the global reaction rate are also shown analytically and
numerically on a two-dimensional square lattice with the periodic boundary
conditions. Especially, the crossover of the global reaction rate is discussed
in both early-time and long-time regimes.
