Beyond 2 3 AU from the Sun, the sputtering by solar wind particles and/or planetary ring particles becomes dominant in the mass loss processes for water-ice grains, compared with the sublimation, and consequently it controls the lifetime of interplanetary dust grains consisting of volatile material. Unfortunately, a lack of sufficient laboratory measurements of sputtering yields of water-ice prevents us from analyzing the behavior of icy grains in such a low temperature region.By using the computer simulation for sputtering processes based on Molecular Dynamics we have estimated the sputtering efficiency of amorphous water-ice cluster consisting of 100 H 2 O molecules by proton impacts with energies from 0.00084 eV to 840 eV. In this simulation, we employ the polarization model (Stillinger and David (1978), Stillinger (1979)) for a water molecule. The standard time step is set to 0.001 fs (1 fs = 10 - 1 5 sec). Although the simulation time is too short to show the relaxation of the cluster, i.e. about 2 x 10 - 1 2 sec after the proton impact to the target, we estimate the proton-energy dependence of sputtering yields at low temperature.