Using first-principles calculations, the insertion and diffusivity of hydrogen in the Ti3Al-D0(13) system are presented and discussed. After a brief description of the properties of Ti3Al, the different sites of insertion are identified and discussed. The octahedral configuration surrounded by Ti atoms only (2a Wyckoff position) is found to be the preferred insertion site for H atoms. The second octahedral and the two tetrahedral sites are found significantly less stable than 2a sites. Phonon, electronic and elastic properties were computed to analyze the interactions between hydrogen and the metal. Results show that hydrogen atoms interact little with the metal. The insertion into a 2a site minimizes the elastic deformation and electronic transfer of surrounding atoms. The diffusion coefficient of hydrogen is then calculated and discussed by using DFT simulations, kinetic Monte-Carlo simulations and a multi-site approach. These results are compared with those of H diffusion into the Ti-hcp and TiAl-L1(0) systems. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.