For the first time, the adsorption of hydrogen on the (110) surface of the A15 Ti3Sb compound with a cubic structure (Cr3Si type; space group Pm3 ̅n) for the accumulation of hydrogen H was calculated using the density functional theory methods (DFT SGGA-PBE). Taking into account the relaxation of the Ti3Sb–H system, the equilibrium positions of hydrogen on the Ti3Sb (110) surface were determined depending on the supercell size. Hydrogen adsorption on the Ti3Sb (110) surface of supercells is preferable in pit sites. The effects of relaxation and an increase in the supercell size (3 × 3 × 3 and 5 × 5 × 5) reduce the adsorption energy compared to the unrelaxed 2 × 1 × 1 supercell. The calculated band structure, curves of local and partial densities of states of Ti3Sb–H are used to explain the interaction of hydrogen with the Ti3Sb (110) surface. The activation energy of H diffusion along the coordinates tetrahedral interstitial site → tetrahedral interstitial site (TIS–TIS) and tetrahedral interstitial site → octahedral interstitial site (TIS–OIS), as well as the diffusion coefficient of H in the cubic lattice of Ti3Sb, were calculated.