We investigated the vibrational density of states (VDOS) of a thin Cu nanowire with < 100 > axial orientation and considered the effect of axial strain. The VDOS were calculated using a real-space Green's function approach with the force-constant matrices extracted from the interaction potential based on the embedded atom method. The VDOS of a strain-free nanowire showed quite distinctive characteristics compared to that of a bulk atom, the most striking feature of which was the existence of high-frequency modes above the top of the bulk phonon spectrum. We further predicted that the low-frequency characteristics of the VDOS would reveal quasi-one-dimensional behavior only when the wire was extremely thin. Through decomposition of VDOS into local atoms, we also exhibited that while the anomalous increase in the low-frequency density of states was mainly due to the corner atoms, the enhancement in high-frequency modes was primarily moderated by core atoms. Additionally, we found that the high-frequency band above the top of the bulk phonon spectrum shifted to higher frequencies, whereas the characteristics at low frequencies remained almost the same upon stretching the nanowire along the axial direction.