We demonstrate the electrically controlled electron transfer of thionine-functionalized reduced graphene oxide (rGO–th) in the form of a homogeneous solution and films. The electron transfer can be realized in a bidirectional way, which provides a method to control the electronic properties of graphene through π–π noncovalent functionalization. Based on the aforementioned controllable electron transfer between graphene sheets and thionine, resistance random access memories with a configuration of Pt/rGO–th/Pt were fabricated and show nonvolatile resistive switching with a large ON/OFF ratio of more than 104, fast switching speed of <5 ns, long retention time of over 105 s and excellent endurance. Furthermore, the reverse electron transfer between thionine and rGO as well as the resistive switching mechanism of the Pt/rGO–th/Pt devices were confirmed by density functional theory (DFT) calculation.