The development of catalysts with high catalytic activity and convenient recycling property is the long-term goal of sulfate-based advanced oxidation processes for the degradation of organic pollutants. In this work, a kind of iron/copper oxide hybrid catalyst (α-Fe2O3/γ-Fe2O3/Cu2O, CuFe-13) with both higher catalytic performance and paramagnetism was synthesized using a modified method for conventional CuFeO2. Through X-ray diffraction and infrared spectra characterization, the catalyst was verified a hybrid of α-Fe2O3, γ-Fe2O3 and Cu2O, in which the exist of magnetic γ-Fe2O3 was the main cause for CuFe-13’s paramagnetism and convenient magnetic recycling property. The mechanism for CuFe-13’s excellent catalytic performance was primarily investigated. Through scanning electron microscope, X-ray photoelectron spectroscopy, N2 adsorption–desorption measurement, radical quenching experiments, and electron paramagnetic resonance characterization analysis, the CuFe-13 represented larger surface area, bigger porosity, more efficient synergistic effect among Cu, Fe, and O than CuFeO2. The generation of various of reactive oxygen species (ROS), including sulfate radical (SO4·-), hydroxyl radical (·OH), and singlet oxygen (1O2), especially 1O2 were more, which might lead to CuFe-13’s higher catalytic performance. The effects of PMS concentration, CuFe-13 dosage, initial pH, initial OG concentration were analyzed. The optimal removal efficiency of OG could be achieved 100% within 20 min with 1 mM PMS and 0.2 g L−1 CuFe-13 under neutral condition. This study provided an efficient PMS-activated catalyst for degradation of organic pollution.