Growth, electronic, and magnetic properties of γ′-Fe₄N atomic layers on Cu(001) are studied by scanning tunneling microscopy/spectroscopy and x-ray absorption spectroscopy/magnetic circular dichroism. A continuous film of ordered trilayer γ′-Fe₄N is obtained by Fe deposition under N₂ atmosphere onto monolayer Fe₂N/Cu(001), while the repetition of a bombardment with 0.5 keV N⁺ ions during growth cycles results in imperfect bilayer γ′-Fe₄N. The increase in the sample thickness causes the change in the surface electronic structure, as well as the enhancement in the spin magnetic moment of Fe atoms reaching  ∼  1.4 μ_B/atom in the trilayer sample. The observed thickness-dependent properties of the system are well interpreted by the layer-resolved density of states calculated using first principles, which demonstrates the strongly layer dependent electronic states within each surface, subsurface, and interfacial plane of the γ′-Fe₄N atomic layers on Cu(001).