The treatment of acidic wastewaters from chemical industries is a difficult task for biodegradation methods to deal with due to the high toxicity and acidity of the waters. Advanced oxidation processes (AOPs) are common methods used for treating refractory wastewaters, but traditional Fenton and ozonation processes are inefficient at pH values below 2. The combination of H2O2-with ozone, termed peroxone reaction, is one potential method to solve this problem because of its high efficiency and ease operation. In this study, a composite comprised of N-doped graphene-CeO2 (NG-Ce) was synthesized as a heterogeneous catalyst in peroxone reaction for the removal of organic pollutants in acidic solutions. X-ray diffraction analysis and Raman spectroscopy confirmed the existence of CeO2 and graphene in the NG-Ce catalyst. X-ray photoelectron spectroscopy was performed to analyze the chemical compositions and the valence states of the elements on the surface of the catalysts. Experimental results showed that NG-Ce greatly improved the oxidative efficiency of peroxone reaction and broadened its working pH range. Although the efficiency of NG-Ce/H2O2/O-3 is decreased as the acidity of solution increases, the degradation of pollutants remained efficient at a pH as low as 0.25. Rich Ce (III) sites on the surface of NG-Ce were suggested to be responsible for the high catalytic activity of NG-Ce in peroxone reaction.