We report on the numerical and experimental study of the vibrational spectrum of the charge-density-wave (CDW) conductor (TaSe 4 ) 2 I. The microscopic mechanism accounting for the giant IR peak at frequencies about 40 cm - 1 in the (TaSe 4 ) 2 I is proposed. The mechanism is based on an assumption about dynamical charge transfer between adjacent CDW periods accompanying their vibration in corresponding normal mode with wave vector equal to that of superstructure. The mechanism is consistent also with the increase in the IR intensity of the peak observed experimentally when heating the (TaSe 4 ) 2 I crystal above the Peierls transition temperature T p = 261 K. Critical index of the Peierls transition order parameter determined from the temperature dependence of the phase phonons intensity is found to be about 0.17, consistent with the results of X-ray experiments.