We present ab initio calculations of the structural, electronic structures, elastic, thermodynamic and vibrational properties of the Ir3Hf compound in the L12 structure. The calculated lattice constants, bulk modulus, and first-order pressure derivative of the bulk modulus are reported for the L12 structure and compared with the earlier values. The elastic constants (C11, C12 and C44) in L12 phase for Ir3Hf compound is calculated using the energy-strain method. The calculated elastic constants satisfy the mechanical stability criterion. Electronic band structures and partial and total densities of states have been derived for Ir3Hf. The band structures show metallic character; the conductivity is mostly governed by Ir 5d states. The phonon-dispersion curves and phonon total density of states based on the linear-response method have been investigated for this compound. Temperature variations of specific heat capacity in the range of 0–1000 K are obtained using the quasi-harmonic model.