The phonon frequencies at the center of Brillouin zone in a series of chiral single-wall carbon nanotubes were calculated numerically, in which the curvature effect was treated appropriately. According to the numerical results, the classification of the vibration modes for chiral tubes at the center of Brillouin zone were analysed. The relations between frequency-chirality and frequency-tube diameter for 12 non-degenerate vibration modes were illustrated.