Using the quasi-harmonic Debye model combine with density functional theory, the lattice structure, elastic constants, polycrystalline moduli, hardness, the Debye temperature θD and heat capacity at constant volume Cv of t-FeAl2 are investigated. The lattice parameters obtained through theoretical simulations are in excellent agreement with the X-ray powder diffraction measurement results. The elastic constants Cij reveal that t-FeAl2 is mechanically stable, with all Cij increasing monotonically as pressure rises. The phonon dispersion curve confirms the dynamical stability of t-FeAl2. Furthermore, the polycrystalline moduli were estimate by the Hill approximation. The ratio of bulk modulus and shear modulus, Poisson's ratio σ and the Vickers hardness Hv under pressure are also calculated. Our results reveal that t-FeAl2 is a hard material with a high Hv that behaves brittlely. Finally, the temperature and pressure-dependence of Cv and θD in the range of 0–1600 K and 0–60 GPa have been obtained and discussed. The results show that the effect of temperature on Cv is more significant than that of pressure, while the pressure has a greater influence on the θD than that of temperature.