The antibiotic level in the aquatic environment has reached threatening levels for human health and ecosystems. Therefore, it is of vital importance to effectively treat antibiotic-containing wastewater. Advanced oxidation processes (AOPs), especially heterogeneous catalytic processes, are considered the most effective process to treat the residual antibiotics in the wastewaters. In the AOPs, activated carbon-supported catalysts have a synergistic effect thanks to the more effective surface area and by transferring electrons to generate radicals through sp2 covalent carbon bond and oxygen functional groups. In this study, oxidative degradation of ciprofloxacin (CIP) in water by persulfate (PS) activated with an activated carbon-supported cobalt-based dual catalyst (Co-AC) synthesized from biomass mixture and cobalt chloride via chemical activation and pyrolysis was examined. The effects of catalyst dosage, contact time, pH, PS concentration and temperature on the performance of the catalyst were investigated in detail. The synergistic effect of the system depending on various combinations (CIP + PS, CIP + Co-AC, CIP + PS + Co-AC) was determined. Co-AC exhibited high catalytic activity in the CIP oxidation with PS activation, even in various water matrices containing some anions such as Cl−, SO42− and NO3−. CIP in the solution could be completely degraded within 120 min in the presence of 0.75 g/L catalyst, 2 mM PS at 25 °C without any pH adjustment. Quenching experiments showed that the Co-AC dual catalyst successfully activated PS to generate SO4•− and •OH radicals, but the SO4•− was more dominant on the CIP degradation. Kinetic analysis of experimental data revealed that the CIP degradation reaction fits the pseudo-first-order kinetics with an activation energy of 62.69 kJ/mol.