Resistive random access memory (ReRAM) devices have been extensively investigated resulting in significant enhancement of switching properties. However fluctuations in switching parameters are still critical weak points which cause serious failures during 'reading' and 'writing' operations of ReRAM devices. It is believed that such fluctuations may be originated by random creation and rupture of conducting filaments inside ReRAM oxides. Here, we introduce defective monolayer graphene between an oxide film and an electrode to induce confined current path distribution inside the oxide film, and thus control the creation and rupture of conducting filaments. The ReRAM device with an atomically thin interlayer of defective monolayer graphene reveals much reduced fluctuations in switching parameters compared to a conventional one. Our results demonstrate that defective monolayer graphene paves the way to reliable ReRAM devices operating under confined current path distribution.