The physical properties including structural, electronic, vibrational and thermodynamic properties of Zr1?x Hfx Co (x is the concentration of constituent element Hf, and changes from 0 to 1) are investigated in terms of the ABINIT program. The results reveal that all of Zr1?x Hfx Co have similar physical properties. When Hf concentration x gradually increases from 0.0 to 1.0, the lattice constant decreases from 3.217 ?A to 3.195 ?A very slowly. The calculated density of states (DOS) indicates that the metallic nature is enhanced and the electrical conductivity tus better with the increase of Hf. Moreover, as Hf concentration increases from 0 to 1, the Fermi energy gradually increases from ?6.96 eV to ?6.21 eV, and the electronic density of states at the Fermi level (N(Ef)) decreases from 2.795 electrons/eV f.u. down to 2.594 electrons/eV f.u., both of which imply the decrease of chemical stability. The calculated vibrational properties show that the increase of Hf concentration from 0 to 1 causes the maximum vibrational frequency to decrease gradually from about 223 cm?1 to 186 cm?1, which suggests a lower dispersion gradient and lower phonon group velocities for these modes. Finally, the phonon related thermodynamic properties are obtained and discussed.