We carry out inelastic electron tunneling spectroscopy (IETS) measurement on a clean Cu(110) surface at 2 K using a scanning tunneling microscope (STM). The spectrum exhibits a single peak at 6 meV, while the phonon density of states (DOS) cannot explain the appearance of this peak. In order to elucidate the origin of the observed peak, we derive a general expression of STM-IETS spectrum for the phonon excitation at a clean metal surface by employing the Keldysh-Green's functional theory. We reveal that the STM-IETS spectrum is proportional to the momentum-resolved Eliashberg function, and not solely to the phonon DOS. By ab initio calculations of the momentum-resolved Eliashberg function combined with the phonon dispersion, we assign the observed peak to the out-of-plane polarized surface phonon mode.