A heterogeneous Fenton-like catalyst with single redox site has a rate-limiting step in oxidant activation, which limited its application in wastewater purification. To overcome this, a bimetallic doping strategy was designed to prepare a heterogeneous Fenton-like catalyst (Fe-Mo/rGO) with a double-reaction center. Combined with electrochemical impedance spectroscopy and density functional theory calculation, it was confirmed that the formation of an electron-rich Mo center and an electron-deficient Fe center through the constructed Fe-O-Mo and Mo-S-C bonding bridges induced a higher electron transfer capability in the Fe-Mo/rGO catalyst. The designed Fe-Mo/rGO catalyst exhibited excellent sulfamethazine (SMT) degradation efficiency in a broad pH range (4.8–8.4). The catalytic performance was hardly affected by inorganic anions (Cl−, SO42− and HCO3−) in the complicated and variable water environment. Compared to Fe/rGO and Mo/rGO catalysts, the SMT degradation efficiency increased by about 14.6 and 1.6 times in heterogeneous Fenton-like reaction over Fe-Mo/rGO catalyst. The electron spin resonance and radical scavenger experiments proved that ·O2−/HO2· and 1O2 dominate the SMT removal in the Fe-Mo/rGO/H2O2 system. Fe and Mo, as active centers co-supported on rGO, significantly enhanced the electron transfer between catalyst, oxidant, and pollutants, which accelerated the reactive oxygen species generation and effectively improved the SMT degradation. Our findings offer a novel perspective to enhance the performance of heterogeneous Fenton-like catalysts by accelerating the electron transfer rate in the degradation of organic pollutants.