Hydrogen diffusion and solubility in disordered alloys are of paramount importance to a variety of practical applications from hydrogen storage materials to separation membranes and protection against hydrogen embrittlement. By employing density functional theory calculations we unveil the atomic-level understanding of hydrogen diffusion in disordered Ti–V–Cr alloys used for hydrogen storage. Hydrogen distribution over interstitial sites of the bcc and fcc lattices of TiV _0.8Cr _1.2 has been simulated using a supercell approach. Taking into account both structural and energy factors we identify tetrahedral sites coordinated by three different metal atoms as the most favorable for hydrogen. The calculations carried out within the nudged elastic band method show that hydrogen diffusion between two tetrahedral site in fcc TiV _0.8.Cr _1.2H _5.25 occurs nearby an intermediate octahedral site with the activation barrier of 0.158 eV for the most probable diffusion pathway. An estimation of the hydrogen diffusion coefficient in fcc TiV _0.8.Cr _1.2H _5.25 at 294 K provides the value of 2.6 × 10 ⁻¹¹ m ²/s that is in fair agreement with experiment data. Despite the modeling was done for a hydride of a definite composition we anticipate that the present results could be extended to Ti–V–Cr hydrides with various compositions.