Molecular dynamics simulations of ice-water interfaces at the supercooling state were performed to elucidate the anisotropic growth kinetics. The simulations were carried out for two kinds of interface orientations, namely, an ice(0001)-water and an ice(10 (1) over bar 0)-water interfaces. It should be emphasized that not only the interface structures but also the growth kinetics are completely different between the interfaces. Furthermore, we analyzed the development of the translational order and the orientational order for the molecular arrangement during the growth. The results suggest that the translational order of the arrangement develops in advance of the orientational order for both interfaces.