The contamination of aquatic environments by organic dye contaminants in industrial wastewater has attracted widespread global attention. The heterogeneous Fenton-like process presents an attractive method for degrading dye pollutants, especially when such reactions are conducted under neutral pH. In this study, Fe2O3/MnO2 composite was employed as a novel heterogeneous catalyst for activating hydrogen peroxide (H2O2) to oxidize and subsequently degrade methylene blue (MB) under neutral pH. Multiple characterization results have confirmed the presence of MnO2 and Fe2O3 as the primary phases of the synthesized compound catalyst. Degradation experiments have demonstrated that the degradation efficiency of MB approaches 100% under the conditions of H2O2 concentration of 0.30% and Fe2O3/MnO2 amount of 0.888 g/L. Furthermore, the Fe2O3/MnO2 catalyst exhibits consistent and outstanding catalytic activity within a broad pH range from 5 to 9 benefiting from the strong interface interaction in Fe2O3/MnO2. The investigation into the kinetics of the Fenton-like reaction indicates that the catalytic degradation of MB by Fe2O3/MnO2 in conjunction with H2O2 follows pseudo-first-order kinetics. Moreover, supplementary scavenging experiments have demonstrated the crucial role played by hydroxyl radicals (·OH) in the catalytic oxidation mechanism of MB. This study offers a promising catalyst for the treatment of dye-containing wastewater under neutral pH condition.