Despite its simple molecular structure, water is still a mystery to scientists. For the atomic and molecular vibrational modes of ice, as is well known, there are two kinds of vibrations: intra-molecular O—H stretching vibration and H—O—H bending vibration within the molecules and three kinds of molecular spatial rotations. However, thirty years ago, a high flux inelastic neutron scattering experiment showed that there are two distinct characteristic peaks in the far-infrared molecular translational vibration region of many ice phases. The origins of these peaks have not been determined till now. In this work, based on the CASTEP code, a first-principles density functional theory plane wave programme, the vibrational spectra as well as the vibrational normal modes of a series of ice phases are investigated. Two kinds of intrinsic hydrogen bond vibrational modes are first found in hydrogen-ordered ice Ic. Then it is found to be a general rule among ice family. Based on the ideal model, we prove that the two vibrational modes can be classified as four-bond vibration and two-bond vibration. There are many coupling modes in-between due to tetrahedral structure deformation under high pressure. Besides, there are also some optical vibrational modes with lower energy in the translational region, such as cluster vibrations and inter-plane vibrations. In Ice VII/VIII and XV/VI, each of which consists of two sublattices, there exist non-hydrogen bond vibrations. These molecular translational vibrations can explain all the far-infrared vibrational spectrum of ice phase, which makes up the last piece of the jigsaw puzzle for the molecular vibration theory of ice. The two vibrational modes do not exist in liquid water due to the collapse of the rigid tetrahedral structure. Thus, a window remains for ice resonance absorption with minimum energy loss in water. This theory is expected to be applicable to industrial deicing, food thawing, gas hydrate mining, and biomolecule frozen molding, etc.