Flexible power sources especially lithium ion batteries (LIBs) have extensively attracted interests in wearable electronics. In these devices, the liquid electrolytes have been replaced by solid polymer electrolytes (SPEs) due to their several advantages such as high specific energy and specific power, non-flammability, nontoxicity and flexibility. In this work, nanocomposite SPEs based on poly(ethylene) oxide (PEO) and lithium perchlorate salt (LiClO4) containing different concentrations of polyethylene glycol-grafted graphene (HFGnP) were prepared via solution blending. HFGnP nanosheets were synthesized by a two-step process, including Hummer’s oxidation and PEG grafting. Polarized optical microscope (POM) and scanning electron microscope (SEM) confirmed the reduction of crystalline regions in nanocomposite electrolytes. In addition, the dissociation factor of salt ions increased upon the addition of PEG-functionalized nanosheets. The ionic conductivity and mechanical properties of nanocomposite SPEs were also considerably enhanced. The flexible LIB based on this nanocomposite electrolyte showed a capacity of 0.126 mAh/cm2 which was three times higher than that of neat SPE. The coulombic efficiency and capacity retention of the flexible batteries were improved by using nanocomposite SPE.