Abstract: Based on the first-principles and quasi-harmonic Debye model, the elastic and thermodynamic properties of BaLiF₃ were investigated.The lattice constant,elastic constants, bulk modulus and shear modulus were calculated under zero-temperature and zero-pressure based on the optimized structure. The results were agreed well with the experimental data and other theoretical values. Then the B/G value of the BaLiF₃ crystal was calculated under zero pressure, and the transition phase point of BaLiF₃ is about 186 GPa, which is accorded with the stability conditions of the crystal. The Debye temperature was calculated at T=300 K by the quasi-harmonic Debye model, and the volume,heat capacity,thermal expansion coefficient α and relative Debye temperature are acquired. It was found that the heat capacity C_V is close to the Dulong-Petit limit under high temperature.