Hydrogen adsorption on HCP Ti (0001), FCC Al (111), and gamma TiAl (100) surfaces is investigated by first principles calculations. Adsorption energy of hydrogen on various sites and energy barrier of diffusion between these sites are derived and compared, to find out the energetically more favorable adsorption site and optimum diffusion path. It is shown that the interaction between H and TiAl surface should be much stronger with lower heat of formation of hydrogen than interaction between H and TiAl bulk, and that the diffusion of hydrogen within the surface layer should be much easier than diffusion from surface to bulk or within bulk layers. Calculation also reveals that it is high energy barrier between various sites which would fundamentally bring about the low diffusion coefficient of H in TiAl bulk. The calculated results are in good agreement with experimental observations in the literature, and could provide a deep understanding of H behavior in gamma TiAl. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved