A proton attachment dynamics to a water cluster is investigated by using a classical molecular dynamics calculation. It is found that three dynamical stages are involved : (1) ultrafast (similar to 10(-14) s) proton attachment to a water molecule of the cluster which followed by (2) the fast (similar to 10(-13) s) sequential proton transfer over several water molecules on the cluster surface and then, (3) the gradual (similar to 10(-11) s) proton penetration to the cluster core. In the first two stages, the large kinetic energy of the order of hundreds kcal/mol is released to the system, which results in the evaporation of a few water molecules from the cluster. The water molecules evaporating in these early stages have large vibrational and translational energies. The mechanism of the energy relaxation and the proton transfer in each process are investigated. The large amplitude vibrational motion promotes sequential concerted proton exchange transfers in the earlier stages (1) and (2). The precise configurational matching of the hydrogen bond coordination and the O-O distance fluctuation are the most important factors to determine the direction and the rate of the proton transfer in the stage (3).