The projector augmented-wave method within the density functional theory is applied to investigate the oxygen diffusion in the intermetallic Ti-Al alloys. It is shown that the highest oxygen absorption energies in Ti-Al alloys correspond to the octahedral Ti-rich sites but the presence of aluminium in the nearest neighbours leads to a substantial decrease in the oxygen absorption energy in the alloys. The migration barriers for the oxygen diffusion between various interstices in the crystal lattice of the Ti-Al alloys are estimated. The preferred migration paths along a and c axes and limiting barriers of the oxygen diffusion in the alloys are determined. The dependence of the oxygen diffusion coefficient on Ti-Al alloy composition is discussed.