We had theoretically studied the energy spectra and group velocities of the acoustic phonons in the rectangular GaN nanowire, covered with elastically dissimilar barriers. It was established that the number of quantum branches increases and spatial degeneracy by wave number q disappears in such wire. The elastic properties of acoustically mismatched barrier influence dramatically the phonon spectrum. The barriers with lower sound velocity (“acoustically slow” barriers) are “compressing” the phonon energy spectrum and strongly reducing the group velocities of the phonons. The barriers with higher sound velocity (“acoustically fast barriers”) demonstrated the opposite effect. The reason for such anomalous, at first look, but strong influence of barrier had been established. In particular, it consists in the re-distribution of the elastic deformations in the heterowire. In the case of “acoustically slow” barriers the wave of elastic deformations in a wide interval of the wave vector retracts into barriers (phonon depletion of the core wire) and spreads there with the velocities corresponding to the acoustic properties of the barrier layers. The opposite situation takes place in the case of “acoustically fast” barriers. It is concluded that these effects can be used in the phonon engineering.