Hydrogen embrittlement is a well-known phenomenon in which hydrogen lowers the strength of materials. Despite extensive investigations, the role of hydrogen in materials remains unclear. Recently, Nagumo proposed the hydrogen-enhanced strain-induced vacancy model, which explains the reduction in the ductility of metals due to a significant increase in the vacancy concentration resulting from plastic deformation in a hydrogen environment. In the present study, we first estimated the interaction energy between hydrogen atoms and an atomic vacancy in alpha iron by applying density functional theory. We then estimated the mobility of an atomic vacancy in a hydrogen environment by calculating the activation energy for diffusion using the climbing image nudged elastic band method. These analyses showed that two hydrogen atoms are trapped by an atomic vacancy under a practical hydrogen gaseous environment (T = 300 K and p = 70 MPa). A reduction in the vacancy formation energy from 2.14 to 1.68 eV and an increase in the activation energy for vacancy diffusion from 0.62 to 1.07 eV by the hydrogen atoms were also observed. Jog dragging by a screw dislocation under shear stress was believed to be the mechanism for vacancy multiplication due to plastic deformation. Using the hydrogen-affected physical properties, we determined the vacancy distribution behind a jog moving at a constant velocity. This analysis suggested that supersaturated vacancies locally accumulate during plastic deformation in hydrogen environments.