Metal-containing Fenton catalysts have been widely investigated. Here, we report for the first time a highly effective stable metal-free Fenton-like catalyst with dual reaction centers consisting of 4-phenoxyphenol-functionalized reduced graphene oxide nanosheets (POP-rGO NSs) prepared through surface complexation and copolymerization. Experimental and theoretical studies verified that dual reaction centers are formed on the C-O-C bridge of POP-rGO NSs. The electron-rich center around O is responsible for the efficient reduction of H2O2 to •OH, while the electron-poor center around C captures electrons from the adsorbed pollutants and diverts them to the electron-rich area via the C-O-C bridge. By these processes, pollutants are degraded and mineralized quickly in a wide pH range, and a higher H2O2 utilization efficiency is achieved. Our findings address the problems of the classical Fenton reaction and are useful for the development of efficient Fenton-like catalysts using organic polymers for different fields.