In this work, the acoustic vibrations of a circular nanowire have been studied on the basis of surface elasticity model, where both the surface elastic property and surface inertia effect are captured. The phonon dispersion and the resonant frequencies for specific vibration modes have been calculated. It has been found from the numerical results that both the surface elastic property and the surface inertia have much effect on the vibration behavior of the nanowire, though depending on the vibration modes. The low-frequency Raman shift has also been considered. The results reveal the surface effect is significant in nanowires, which may make it possible to use Raman scattering to determine the surface properties.