As is well known, hydrogen plays an important role in degrading mechanical properties of steel due to hydrogen embrittlement behavior. Thus, much attention should be paid to the interaction between hydrogen atom and Fe matrix especially in theoretical calculation and mechanism study. In this paper, the site occupations of hydrogen atom under different single axis strains in interstitial of α-Fe atoms are studied by the first principles calculation based on the spin-polarized density functional theory. The Kohn-Sham equations are solved under periodic boundary conditions, by using revised Perdew-Burke-Ernzerhof version of the generalized gradient approximation to account for the electron exchange and correlation. The total energy of the steady state crystal, binding energy, solution energy, density of states, charge density difference and charge population are calculated. The analyses of solution energy and density of states indicate that the hydrogen atom preferentially occupies the tetrahedral interstitial of α-Fe atoms under different single axis strains. With increasing tensile strain or reducing compressive strain, hydrogen atom prefers to occupy the site of tetrahedral interstitial. The analyses of charge population and charge density difference reveal that the hydrogen atom collects charges from Fe atoms, leading to electron density redistribution. The tensile strain reduces the charge transfer slightly while the compressive stress promotes the transfer process. The LST/QST (linear synchronous transit/quadratic synchronous transit) transition state search method is used to investigate the diffusion of hydrogen atom between two tetrahedral interstitials along the direction perpendicular to strain. Diffusion of hydrogen atom goes through transition state where the hydrogen atom is coordinated at octahedral interstitial. The minimum energy pathway for hydrogen diffusion under strainless state indicates the diffusion activation energy with a value of 0.58 eV. It is noticeable that the diffusion activation energy and the strain conforms to linear relation and are consistent with the fitting formula, Q=0.508+2.6ε. The diffusion activation energy increases with reducing compressive strain or increasing tensile strain. According to the calculation process and analysis results, we introduce the interaction between hydrogen atom and α-Fe at a level of electronic structure systematically and figure out the diffusion of hydrogen influenced by different states of stress.