The treatment of acid wastewater to remove organic matter in acid wastewater and recycle valuable resources has great significance. However, the classical advanced oxidation process (AOPs), such as the Fenton reaction, encountered a bottleneck under the conditions of strong acid. Herein, making use of the oxidation properties of CeAY (CeO2@acid clay), we built an AOPs reaction system without H2O2 under a strong acid condition that can realize the transformation of organic matter in industrial wastewater. The X-ray photoelectron spectroscopy (XPS) proved that the CeAY based on Ce3+ as an active center has abundant oxygen vacancies, which can catalyze O2 to produce reactive oxygen species (ROS). Based on the electron spin-resonance spectroscopy spectrum and radical trapping experiments, the production of •O2- and •OH can be determined, which are the essential factors of the degradation of organic compounds. In the system of pH = 1.0, when 1 mg CeAY is added to 10 mL of wastewater, the degradation efficiency of an aniline solution with a 5 mg/L effluent concentration is 100%, and that of a benzoic acid solution with a 100 mg/L effluent concentration is 50% after 10 min of reaction. This work may provide novel insights into the removal of organic pollutants in a strong acid water matrix.