We presented a detailed first-principal calculation to study the structural, elastic, dynamical, and thermal properties of a new synthetic ternary zinc nitride semiconductors CaZn 2 N 2 using the generalised gradient approximation (GGA) method. The obtained lattice parameters of CaZn 2 N 2 at 0 K and 0 GPa are in good agreement with the experimental data and other theoretical findings. The pressure dependences of the elastic constants C ij together with other derived mechanical properties of CaZn 2 N 2 compound have also been systematically investigated. The results reveal that CaZn 2 N 2 is mechanically stable up to 20 GPa. The calculated the phonon curves and phonon density of states under different pressures indicate that the CaZn 2 N 2 compound maintains its dynamical stability up to 20 GPa. An analysis in terms of the irreducible representations of group theory obtained the optical vibration modes of this system, and we obtained the frequencies of the optical vibrational modes at Г points together with the atoms that contributed to these vibrations of CaZn 2 N 2 . Meanwhile, the pressure dependencies of the frequencies Raman-active and IR-active modes at 0–20 GPa have been studied. The quasi-harmonic approximation (QHA) was applied to calculate the thermal properties of CaZn 2 N 2 as functions of pressures and temperatures such as the heat capacity, thermal expansions, the entropy, and Grüneisen parameter γ .