Catalytic activity of graphene and its related compounds have been reported in the ozonation process. In addition, Fe3O4 has a good catalytic activity in the ozonation process. Fabrication of high porosity Fe3O4/graphene oxide nanohybrids can improve the production of reactive oxygen species. Mesoporous Fe3O4/ graphene oxide nanohybrid was prepared by coprecipitation method. The catalytic activity of nanohybrid was investigated in ozonation degradation of acid red88 in the simulated wastewater. The progress of degradation process was determined using reactive oxygen species scavengers. The process was modeled by the artificial neural network. The mesoporous nanohybrid has a specific surface area of 252.7 m2/g, total pore volume of 0.353 cm3/g and mean pore diameter of 5.6 nm. Fe3O4/ graphene oxide showed superior catalytic activity compared to Fe3O4 and graphene oxide. Hydroxyl (OH·) and superoxide radicals were identified the main radical reactive species. The influence of ozone dosage, pH, dye and catalyst concentration, on the acid red88 degradation rate was investigated. The degradation process was pH dependent, and acidic condition was more favorable to mineralization of acid red88 than neutral or basic mediums. Chemical oxygen demand removal has reached 69% in the catalytic ozonation process, while it reached only 25% in single ozonation process. A very good agreement (R = 0.99) was observed between the calculated and experimental degradation efficiency. The results demonstrated that mesoporous nanohybrid is a promising catalyst for ozonation process, especially treating water polluted by azo dyes.