The mechanism of the excess-proton transfer in ice is investigated by analyzing the potential energy surface, the normal modes, and the interaction between the excess proton and defects. It is found that the solvation from water molecules in long-distance shells is essential for the smooth transport of the proton. The solvation shells up to, for example, about the 18th shell are needed to attain a convergence of the excess-proton solvation energies. The potential energy surface of the excess-proton transfer calculated with including these distant hydration shells is very smooth even for a long distance proton transport. Normal modes are calculated along the reaction paths of the proton transfer. An analysis is done to find how the character of these normal modes changes along the proton transfer. The structure and energetics of hydronium ion and L-defect complex are also examined to explain the temperature dependence of the proton transport.