Ice(0001)/water and ice{<10(1)over bar 0>})/water interfaces were studied by means of molecular dynamics simulation. The anisotropy in the growth kinetics, that is, the difference in the growth kinetics between the interfaces was observed in the molecular level for the first time; the growth for the ice{0001}/water interface occurred by the kinetics of layer by layer, and that for the ice{<10(1)over bar 0})/water interface occurred by the kinetics of collected molecule process. Moreover, the molecular-scaled structures of the interfaces were investigated. As a result, it was made clear that the structure of the ice{0001}/water interface was smooth, but that of the ice{<10(1)over bar 0>}/water interface was rough. Finally, the relationship between the anisotropic interface structures and the anisotropic growth kinetics was discussed.