We have measured the surface phonon dispersion curves on the hydrogen-terminated Si(110)-(1×1) surface with the two-dimensional space group of p2mg along the two highly symmetric and rectangular directions of ΓX and ΓX' using high-resolution electron-energy-loss spectroscopy. All the essential energy-loss peaks on H:Si(110) were assigned to the vibrational phonon modes by using the selection rules of inelastic electron scattering including the glide-plane symmetry. Actually, the surface phonon modes of even-symmetry to the glide plane (along ΓX) were observed in the first Brillouin zone, and those of odd-symmetry to the glide plane were in the second Brillouin zone. The detailed assignment was made by referring to theoretical phonon dispersion curves of Gräschus et al. [Phys. Rev. B 56, 6482 (1997)]. We found that the H-Si stretching and bending modes, which exhibit highly anisotropic dispersion, propagate along ΓX direction as a one-dimensional phonon. Judging from the surface structure as well as our classical and quantum mechanical estimations, the H-Si stretching phonon propagates by a direct repulsive interaction between the nearest neighbor H atoms facing each other along ΓX, whereas the H-Si bending phonon propagates by indirect interaction through the substrate Si atomic linkage.