For the yttrium orthovanadate with a tetragonal zircon-type structure, the first complete set of Raman-active and IR-active phonon modes has been calculated using ab initio density functional perturbation theory. The calculated IR reflectivity spectra are in good agreement with available experimental data. We report the calculated frequencies of three Raman-active modes that could not be detected experimentally and a new assignment of the experimental Raman data. The contributions of each IR-active phonon modes to static dielectric tensor have been determined.