Currently, the designations for the low-frequency vibrational spectrum of liquid water are still diversified. In this Letter, using the instantaneous normal mode (INM) formalism for subensembles, we have examined the effects of local structure on the low-frequency INM spectrum of liquid water. The classified subensembles of water molecules are characterized by either the geometry of Voronoi polyhedron or the H-bond configuration. With these subensembles, the translational contribution to the INM spectrum is investigated. Providing insights into the local structural dependence of the vibrations between H-bonded water molecules, our results are consistent with the conventional designations for the Raman spectrum of liquid water.