Recent advances in information technology require the flexible, lightweight, and low power electronics in various applicatino areas. In particular, the development of low power flexible memory is necesary due to its privotal roles in all modern electronic systems. As a promising next-generation flexible nonvolatile memory, we have investigated the memory characteristics of poly(1,3,5-trimethyl-1,3,5-trivinyl cyclotrisiloxane) (pV3D3) deposited via initiated chemical vapor deposition (iCVD) process, which provides a solvent-free and low-temperature deposition of highly uniform polymer films on various substrates. The Cu/pV3D3/Al RRAM device show the unipolar resistive switching with a high on/off ratio, and reliable retention characteristics, but high reset power consumption, and nonuniform resistive switching uniformity issues remain to be addressed for reliable low power memory application. To address these problems, we introduced a multilayer graphene (MLG) film as Cu diffusion barrier, which suppresses the diffusion of Cu ions through pV3D3 films, resulting in the ultra-low reset current due to the high out-of-plane resistance of MLG. In addition, the high thermal conductivity of graphene suppresses the reset process by Joule heating and a high interfacial resistance at the pV3D3/MLG induces the formation/rupture of Cu filament at the interface by electrochemical redox reaction, improving the nonuniform resistive switching uniformity. The innovative approach presented in this work can pave the way of a new area of application for graphene toward low power nonvolatile memory.