We performed molecular dynamics calculations of surface of ice Ih in order to investigate formation mechanism of melting layer on the surface. The results showed that the vibrational amplitude of the atoms in the surface layer greatly depends on the crystal orientation, whereas that in the ice bulk is isotropic. The anisotropy of the vibration is due to a dangling motion of the free O-H bonds exist at the surface layer. The dangling motion enhances the rotational motion of the water molecules. The vibrational density of state showed a coupling between the rotational vibration and the lattice vibration of the water molecules in the surface layer. The coupling of the vibrations causes a distortion of ice lattice. Through the hydrogen-bonding network, the distortion transmits to the interior of the crystal. We conclude that the dangling motion of the free O-H bonds exist at the surface layer is one of the dominant factors governing the surface melting of ice crystal. (C) 2004 American Institute of Physics.