In this paper, the diffusion of the hydrogen atom in alpha-Fe under an applied 3-axis strain was investigated by the thermodynamics analysis and density functional theory calculations. The quantum manifestations of the hydrogen diffusion were presented, and were well explained by putting the quantum electronic stress and the zero point energy of the hydrogen atom into the thermodynamics model. It indicates that the quantum effects are dominant for the hydrogen atom diffusion in the strained alpha-Fe. The diffusion barrier energy increases and the diffusion coefficient decreases with the decreasing compressive strain or increasing tensile strain. The charge density difference was also calculated to reveal the physical insight of the effect of strain on the hydrogen diffusion in alpha-Fe. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.