As an important uranium alloy, U-Mo alloy has excellent mechanical properties, structural stability and thermal conductivity, which an important nuclear reactor fuel and tank armor. However, there is a serious fundamental problem of U-Mo alloy which requires several considerations in practical application. U-Mo alloy is easily subjected to surface corrosion of small molecules including the H<sub>2</sub>, O<sub>2</sub>, H<sub>2</sub>O, CO<sub>2</sub> and so on. The hydrogen corrosion and oxidation will have significant influence on it. In order to further investigate the reaction mechanism, based on the density functional theory and the transition state algorithm, the first principles calculation of γ-U (100) with Mo atom doping and Mo coating are investigated. Firstly, the minimum energy path of H<sub>2</sub> molecule is calculated for the dissociation adsorption on Mo-U and 4Mo-U surface; Secondly, the transition states of H and O atoms are studied surface diffusing between adjacent most stable adsorption sites; Thirdly, the bulk phase diffusion of H and O atoms is investigated and the relationship are analyzed between adsorption energy and adsorption height in the bulk phase diffusion. The results show that when H<sub>2</sub> molecule is adsorbed at the configuration of top horizontal, the H atom needs to overcome a barrier to H-H bond-broken and then is adsorbed on surface bridge site with the neighboring atoms. The energy barrier for H<sub>2</sub> dissociation on 4Mo-U is more than that of Mo-U. Meanwhile, the lower energy barrier required for O atom to diffuse in Mo-U, so that it can be adsorbed, dissociated and diffused quickly, and then form an oxidation film on the surface. Furthermore, both H and O atoms need to cross the energy barrier to diffuse into the body phase, form chemical bonds with the atoms and present in the body phase stably finally. In this paper, the dissociation and diffusion of the initial stage for hydrogen corrosion and oxidation on uranium-molybdenum alloy are comprehensively analyzed by theoretical studies. The results lay a foundation for exploring the surface corrosion mechanism of U-Mo alloy by theoretical method. Meanwhile, it provides theoretical support for investigating burn-in and corrosion of uranium-molybdenum alloy, predicting material properties under extreme and special environment, and provides reference for further research on corrosion resistance of uranium-molybdenum alloy.