The application of nanoparticle heterogeneous Fenton-like catalysts is limited due to the requirement of filtration after reaction and possible secondary pollution. In this work, a novel mesh-type monolithic Fenton-like Cu/Fex/γ-Al2O3/Al catalyst was developed for the degradation of dyes. The Cu and Fe species are uniformly dispersed on the mesh-type anodic monolithic γ-Al2O3 supports, and the results of scanning electron microscopy and X-ray diffractometry analysis show that Fe can reduce the particle size of Cu over γ-Al2O3. The activity results show that the degradation rate of rhodamine B (RhB) reached 99.5% within 1 h using 4 × 6 cm Cu12.0/Fe2.0/γ-Al2O3/Al catalyst with 1,200 ppm H2O2 at 50 °C. The important role of •OH as a reactive oxidant was confirmed through electron spin-resonance spectroscopy and radical scavenging experiment. The hydrogen temperature programmed reduction suggests the high redox ability of Cu/Fe bimetallic catalyst is beneficial to the production of •OH. The Cu/Fe bimetallic catalyst shows excellent recyclability in a 10-cycle experiment, the degradation rate of RhB was maintained at 98% and the leaching amount of metals was lower than 0.7 mg/L. The mesh-type catalyst will be easily applied for the continuous wastewater treatment because it does not need filtration for recovery.