This paper studies the effect of the temperature-depended interface kinetics on the morphological stability of a spherical particle under the non-equilibrium solidification condition. The result shows that as the interfacial kinetics parameter increases, the growth velocity of the spherical particle decreases. Compared with the case of neglecting interfacial kinetics, the temperature-depended interfacial kinetics has the significant stable effect on the morphological stability of the spherical crystal and the critical stability radius increases as the interfacial kinetics parameter increases. (C) 2012 Published by Elsevier B.V.