Consumption of additional H2O2 is necessary in classical Fenton catalysis. Herein, we report a novel and special nanocatalyst consisting of CoMoS2 nanosphere-embedded, reduced graphene oxide (rGO) nanosheets (CMS-rGO NSs). This nanocatalyst was discovered to have an impressive reactivity for in situ generation and synchronistical activation of H2O2 in different active centers, yielding fast and efficient degradation of the pollutants. The reaction rate is similar to 21 times higher than that of conventional Fenton catalysts. The characterization shows that countless flower-like CoMoS2 nanospheres are uniformly embedded in the rGO nanosheets through Mo-S-C bonding bridges in CMS-rGO NSs, which leads to activation of the pi electrons and their transfer from rGO to the metal centers (pi -> M). The formed Mo-O-Co further leads to a distribution of orientations of the electrons around the metal centers due to the different electronegativity of Mo and Co. During the reaction, the dissolved O-2 is efficiently reduced to HO2 center dot/O-2(center dot-) around the electron-rich Mo center, and HO2 center dot/O-2(center dot-) is further reduced to H2O2 around the Co center. The generated H2O2 is finally reduced to (OH)-O-center dot for degrading dyes in the electron-rich metal (Mo or Co) centers of CMS-rGO NSs. The dye pollutants also act as electron donors, and they are directly degraded in the electron-poor pi-center of CMS-rGO NSs, which promote the electron transfer cycle and achieve electron gain-loss balance. This discovery provides a new strategy for H2O2 generation-activation and pollutant degradation through constructing electron transfer bridges over the surface of catalysts. (C) 2019 Elsevier Inc. All rights reserved.