Using the first-principles full-potential linear muffin-tin orbital method in the atomic sphere approximation, we have calculated the electronic structure of the intermetallic compound , and evaluated the electric field gradients (EFGs) at all of the three inequivalent positions (two Hf and one Fe) in its lattice. The main results extracted from the experimental investigations, concerning the different magnitudes and origins of the EFGs at inequivalent Hf sites, are correctly reproduced. The possible mechanisms of formation of the EFGs at these sites are analysed and discussed.