To predict hydrogen embrittlement in steels and clarify its mechanism, it is necessary to understand the time variation of hydrogen distribution. Since the quantum mechanical effect is remarkably observed in hydrogen diffusion, even at room temperature, there is a need to take into account it for analyses. In this study, we evaluated the diffusion coefficients of hydrogen in body-centered cubic (bcc) iron via density functional theory and small-polaron theory calculations. The analyses were carried out under various magnitudes of volumetric strains to investigate its effect on the diffusion coefficient. The temperature dependence of the diffusion coefficient was found to change at about 400 K. This is attributed to the fact that the tunneling between ground states dominantly contributes to the diffusion at lower temperatures, whereas at high temperatures, that between low excited states contributes dominantly. The diffusion coefficient was also found to increase with compressive volumetric strain and decrease with tensile volumetric strain. The volumetric strain dependence of the diffusion coefficient was clarified by the volumetric strain dependence of the tunneling matrix elements and that of the activation enthalpy.