We carried out molecular dynamics simulations of interstitial water molecules in ice to clarify behavior and vibrational properties of self-interstitials in ice. We used an atom-atom potential model developed by Kumagai er al. [N. Kumagai, K. Kawamura and T. Yokokawa, Mel. Sim. 12, 177 (1994)] which allows intramolecular motions. We confirmed high reliability of the potential model for reproducing the structure and vibrational spectra of ice. From trajectory observations of self-interstitials, we found that a stable interstitial site is an uncapped trigonal site. By comparing power spectra of vibrational motions for self-interstitials with that of matrix ice, we found that the large formation entropy of the interstitial molecule is attributed to much higher density of states in a low frequency region for the interstitial than that for the matrix.