We have investigated the effect of piezoelectric (PZ) polarization property on group velocity of phonons in binary as well as in ternary wurtzite nitrides. It is found that with the presence of PZ polarization property, the phonon group velocity is modified. The change in phonon group velocity due to PZ polarization effect directly depends on piezoelectric tensor value. Using different piezoelectric tensor values recommended by different workers in the literature, percent change in group velocities of phonons has been estimated. The Debye temperatures and frequencies of binary nitrides GaN, AlN, and InN are also calculated using the modified group velocities. For ternary nitrides Al (x) Ga((1-x))N, In (x) Ga((1-x))N, and In (x) Al((1-x))N, the phonon group velocities have been calculated as a functions of composition. A small positive bowing is observed in phonon group velocities of ternary alloys. Percent variations in phonon group velocities are also calculated for a straightforward comparison among ternary nitrides. The results are expected to show a change in phonon relaxation rates and thermal conductivity of III-nitrides when piezoelectric polarization property is taken into account.