Filament type resistive random access memory (RRAM) based on polymer thin films is a promising device for next generation, flexible nonvolatile memory. However, the resistive switching nonuniformity and the high power consumption found in the general filament type RRAM devices present critical issues for practical memory applications. Here, we introduce a novel approach not only to reduce the power consumption but also to improve the resistive switching uniformity in RRAM devices based on poly(1,3,5-trimethyl-3,4,5-trivinyl cyclotrisiloxane) by inserting multilayer graphene (MLG) at the electrode/polymer interface. The resistive switching uniformity was thereby significantly improved, and the power consumption was markedly reduced by 250 times. Furthermore, the inserted MLG film enabled a transition of the resistive switching operation from unipolar resistive switching to bipolar resistive switching and induced self-compliance behavior. The findings of this study can pave the way toward a new area of application for graphene in electronic devices.