Hydrogen penetration into iron sheets from a borate buffer solution (pH 8.4) was investigated using a modified Devanathan-Stachurski cell with flow paths. A sinusoidal perturbation method was applied to evaluate the hydrogen-diffusion coefficient D and its dependence on specimen thickness, polarization potential, and electrolyte flow rate. A fast Fourier transform (FFT) technique was employed to achieve automated derivation of the diffusion coefficient with precision and rapid screening of the experimental conditions. The obtained value of D increased with an increase in the specimen thickness or with an increase in the overpotential of the hydrogen evolution reaction, indicating the effect of a surface barrier layer-like oxide film on the hydrogen-entry side. On the other hand, D is not dependent on the electrolyte flow rate in the entry-side cell. From the viewpoint of hydrogen penetration, the properties of the barrier layer are almost immune to the flow rate, though it is affected by the polarization potential. The sinusoidal perturbation method combined with FFT allows the time-dependent evaluation of the hydrogen-penetration behavior in specimens with temporal changes, such as oxide-film formation and corrosion.