Cu-Al2O3-g-C3N4 and Cu-Al2O3-C-dots were synthesized for the first time to enhance the catalytic activity and utilization of H2O2. SEM, TEM, XPS, FT-IR, XRD, TPR and solid-state EPR were used to characterize the catalysts. In the Cu-Al2O3-g-C3N4 system, the electron-rich centre of Cu and electron-deficient site of Al were formed due to the higher electronegativity of Cu. Moreover, Cu ions could coordinate with the hydroxyl on the tri-s-triazine ring of g-C3N4 or the graphene conjugated pi-domains of C-dots via the Cu-O-C linkage so that the orbital interactions involving electron transport from pi -> Cu also induced the formation of an electron-rich Cu centre and an electron-deficient n-electron conjugated system, resulting in the strengthening of the dual-reaction centres. This mechanism was validated by Roman, EPR and XPS spectra. In addition, EPR experiments demonstrated that two electron-transfer processes formed center dot OH in the presence of H2O2. The first electron transfer was from the electron-rich Cu centres to H2O2, and the other was from H2O to the electron-deficient site. Thus, more center dot OH were generated and high H2O2 utilization was achieved in the Cu-Al2O3-g-C3N4 and Cu-Al2O3-C-dots suspension. Furthermore, the turnover frequency (TOF) for the Cu-Al2O3-C-dots and Cu-Al2O3-g-C3N4 dispersions were determined and were found to be much higher than those of the classic homogeneous Fenton reaction. Thus, Cu-Al2O3-g-C3N4 and Cu-Al2O3-C-dots showed high activity and stability for the catalytic degradation of organic pollutants under mild conditions.