The vibrational structure of chromium germanium telluride (Cr₂Ge₂Te₆, CGT) is investigated and a strong spin-phonon coupling is revealed. The measured high-resolution Raman scattering (RS) spectra are composed of the 10 Raman-active modes: 5Ag and 5Eg, predicted by calculation using the density functional theory and identified using polarization-resolved RS measurements. We also studied the effect of temperature on the RS spectra of CGT from 5 K to 300 K. A strong magneto-phonon coupling in CGT is revealed at temperatures of about 150 K and 60 K, which are associated with the appearance of the local magnetic order in the material and the transition to the complete ferromagnetic phase, respectively. Moreover, a unique shape of the A_g⁵ mode composed of a set of very narrow Raman peaks is simulated using a model that takes into account vibrations of Ge-Ge pseudo-molecules for various Ge isotopes.