Utilizing density functional and perturbation theory, combined with ab initio molecular dynamics methods, we investigate the phonon and vibrational properties, mechanical and thermodynamic characteristics, as well as melting points of the tetragonal and cubic phases of anti-perovskite nitride Cr3GeN. Our findings demonstrate that the cubic phase is stable at high temperatures but exhibits the softening of the optical phonon mode at the Brillouin zone center at low temperatures, thereby transforming into the tetragonal phase. Both the tetragonal and cubic phases exhibit mechanical robustness and satisfy the conditions for mechanical stability. As a metallic compound, the anti-perovskite Cr3GeN additionally possesses high hardness and melting point, thus stimulating high hardness and temperature applications.