The maximal entropy production principle was applied to model the growth kinetics of a multi-component stoichiometric compound. Compared with the solid-solution phase and the non-stoichiometric compound, the dissipation by the trans-interface diffusion makes the interface slow down by decreasing the effective interface mobility and does not result in solute trapping or disorder trapping. An application to the crystallization of a CuZr stoichiometric compound shows that the transition from the thermodynamic-controlled to the kinetic-controlled growth can be predicted.