The three-dimensional distribution function (DF) and the potential of mean force (PMF) of water and hydronium ions in five protonated states of the influenza A M2 channel are calculated by means of the three-dimensional reference interaction site model (3D-RISM) theory in order to clarify the proton conduction mechanism of the channel. Each protonated state, denoted as iH, where i = 0-4, has a different number of protonated histidines, from 0 to 4. The DF of water in each state exhibits closed structures of 0H, 1H, and 2H and open structures in 3H and 4H. In the closed form, the DF and PMF indicate that hydronium ions are excluded from the channel. In contrast, the ion can distribute throughout the opened channel. The barrier in PMF of 3H, approximately 3-5 kJ/mol, is lower than that of 4H, 5-7 kJ/mol, indicating that 3H has higher permeability to protons. On the basis of the radial DFs of water and hydronium ions around the imidazole rings of His37, we propose a new mechanism of proton transfer through the gating region of the channel. In this process, a hydronium ion hands a proton to a non-protonated histidine through a hydrogen bond between them, and then the other protonated histidine releases a proton to a water molecule via a hydrogen bond. The process transfers a proton effectively from one water molecule to another.