Copper oxides were supported on the surface of defect-containing g-C₃N₄ (d-g-C₃N₄–Cu) by alkalization and hydrothermal methods and characterized using a variety of techniques and density functional theory (DFT) calculations. It was verified that dual reaction centers were constructed by the complexation of–C₁N₁–Cu linkages between Cu of copper oxides (CuO_x) and cyano (–C₁N₁) groups of the side chain in the tri-s-triazine ring of d-g-C₃N₄, which formed electron-rich centers around Cu sites and electron-poor centers around C₁ sites. Based on the experimental results, it was established that the Fenton-like process took place with H₂O₂ being mainly reduced to hydroxyl radicals (˙OH) by the electrons from electron-rich Cu centers, while both OH⁻ and pollutants were adsorbed on the C₁ sites, and could be oxidized to donate electrons to Cu centers by electron transfer of π → Cu in –C₁N₁–Cu, maintaining charge balance on the d-g-C₃N₄–Cu. Thus, the catalyst was highly efficient for the degradation of various refractory organic pollutants in water of pH from 3 to 10; moreover, higher pH resulted in higher reaction efficiency because more adsorbed OH⁻ at C₁ sites produced more ˙OH. Our findings indicate that the dual-reaction-center Fenton-like process is very promising for environmental remediation.