The absorption and diffusion of oxygen in the Ti₃Al alloy are studied by the projector augmented wave within the density functional theory. The highest absorption energies are shown to correspond to the sites in the octahedra formed by six titanium atoms, and the presence of aluminum in the nearest neighbors leads to a substantial decrease in the binding energy of oxygen in the alloy by approximately 1.5 eV. The energy barriers of oxygen diffusion between various interstices in the crystal lattice of the alloy are estimated, and the preferred migration paths in the (0001) plane and the [0001] direction are determined. It is found that the migration barrier from the most preferred octahedral O1 site to distorted tetrahedral Ti-site (2.42 eV) is a key barrier and limits the oxygen diffusion in the alloy. The calculated temperature diffusion coefficient of oxygen in the Ti₃Al alloy and the activation energies determined in two directions agree with the experimental data.