In this study, the synthesized CuCo-zeolitic imidazolate framework (ZIF) catalyst was used to degrade methyl orange (MO) and methylene blue (MB) in water via a novel Fenton-like catalytic reaction. Effects of catalyst dosage, H2O2 concentration, initial concentration of the contaminants, and reaction time were evaluated. The results showed that MO and MB decomposition efficiencies were highly influenced by CuCo-ZIF concentration. The presence of H2O2 accelerated the degradation reaction of both MO and MB. Although it took 100 min to complete the removal of MB, it was 60 min for MO. At concentrations of MO and MB lower than 40 mg·L−1, the catalyst showed an almost complete degradation. The CuCo-ZIF catalyst presented a good recyclability with more than 90% removal of MO and MB after four times and five times reuse, respectively. These results demonstrated that MO and MB were efficiently degraded by a Fenton-like catalyst of CuCo-ZIFs and its potential in industrial wastewater treatment.