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γ-Fe₂O₃ is considered to be a promising catalyst for the selective catalytic reduction (SCR) of nitrogen oxide (NO_x). In this study, first-principle calculations based on the density function theory (DFT) were utilized to explore the adsorption mechanism of NH₃, NO, and other molecules on γ-Fe₂O₃, which is identified as a crucial step in the SCR process to eliminate NO_x from coal-fired flue gas. The adsorption characteristics of reactants (NH₃ and NO_x) and products (N₂ and H₂O) at different active sites of the γ-Fe₂O₃ (111) surface were investigated. The results show that the NH₃ was preferably adsorbed on the octahedral Fe site, with the N atom bonding to the octahedral Fe site. Both octahedral and tetrahedral Fe atoms were likely involved in bonding with the N and O atoms during the NO adsorption. The NO tended to be adsorbed on the tetrahedral Fe site though the combination of the N atom and the Fe site. Meanwhile, the simultaneous bonding of N and O atoms with surface sites made the adsorption more stable than that of single atom bonding. The γ-Fe₂O₃ (111) surface exhibited a low adsorption energy for N₂ and H₂O, suggesting that they could be adsorbed onto the surface but were readily desorbed, thus facilitating the SCR reaction. This work is conducive to reveal the reaction mechanism of SCR on γ-Fe₂O₃ and contributes to the development of low-temperature iron-based SCR catalysts.