The mechanism of proton transfer in ice is investigated theoretically by examining the potential energy surfaces and determining the reaction coordinates. It is found to be quite different from that in liquid water. As shown by many authors, proton transfer in liquid water is promoted by the structure fluctuation, creating three-coordinated water molecules in the hydrogen bond network rearrangement, and the excess proton makes transitions among these three-coordinated water molecules as forming a so-called Zundel structure, (H5O2)(+). This kind of large structural rearrangement cannot take place in ice. Nevertheless, the proton transfer in ice can be very fast. It is found that the strong constraint on the molecular geometry in ice is the source of the facile proton transfer. This constraint reduces the stabilization of the excess proton state in two ways: (1) as O-O cannot shrink freely, it cannot form a stable Zundel structure in which two water molecules share the excess proton locating at the center of the shortened O-O bond, and (2) as the existence of the repulsive force, an Eigen structure cannot be much stabilized. This repulsive force also contributes to partially shorten the O-O distance and thus facilitating a proton transfer. As the result, the excess proton is not trapped in a deep energy minimum but makes the transfers on small energy barriers. The molecular geometry relaxation along the proton transfer is analyzed; it is found that O-O stretchings/shrinkages at the excess proton moiety are mutually coupled to assist the sequential proton transfers in a concerted fashion. The energetics and geometrical changes along these reaction coordinates are analyzed. The potential energies are found to be fairly flat for different locations of the excess proton. The nature of the excess proton solvation from the surrounding water molecules are analyzed; it is shown that the solvation by even distant shells yields a significant contribution to the potential energy surface of the proton transfer.