Based on first-principles calculations, the binding energy of hydrogen atom to Y2O3 and Y2O3|bcc Fe interface (relative to bcc Fe side) with cube-on-cube orientation is at least 0.45 eV, if hydrogen substitutional is considered, or at least 0.26 eV if only hydrogen interstitial is considered. The calculated binding energies do not have a unique fixed value, because they are dependent on the interface structure, the Fermi level of Y2O3 near the interface and the chemical potential of Y/O. Hydrogen substitutional is more stable than hydrogen interstitial near the interface for Fermi level around calculated Schottky barrier height (SBH) at equilibrium. The Y2O3 particle interior can be an effective trapping site for hydrogen. Hydrogen interstitial, hydrogen substitutional and Y/O vacancy have a much lower energy near the interface than within the Y2O3 particle, presumably due to image charge interaction related to their non-zero charge state. For neutral impurities or defects, the energy near interface and that far away from the interface are similar (⩽0.1 eV difference) for a perfect coherent interface. The Y2O3|bcc Fe interface should provide effective trapping sites for hydrogen atoms in oxide dispersion strengthened (ODS) steels.