The acoustic wave propagation in the hexagonal structured ZnTe nanoparticles has been studied at room temperature. In this paper, the orientation dependence of three types of acoustic wave velocity and Debye average velocity have been calculated using second order elastic constants. The six second order elastic constants are calculated for ZnTe at 300 K using Lenard-Jones Potential. An anomalous behaviour in orientation dependent acoustic wave velocity is obtained which is due to the combined effect of elastic constants and density. These velocity data are important for their structural information and to differentiate them from other nanostructure materials and other compounds. Obtained results, together with other well known physical properties, may expand future prospects for the applications and study of this nano material.