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Electrochemical Double-Layer Capacitors (EDLCs) afford low specific capacitance when graphene structure has high degree of graphitization and defect. In this study, a novel, facile and economical electrochemical exfoliation method is used for the straightforward fabrication of graphene from graphite electrode under ambient conditions. Successful fabrication of graphene structures is verified via X-ray diffraction (XRD), Raman and FT-IR spectroscopy. The morphology of the prepared samples is studied using Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). The electrochemical performances of the as-prepared graphene show excellent specific capacitance (210 F/g) for the sample synthesized in the lowest electrolyte concentration being several times higher than that of the initial graphite electrode (~26 F/g). The optimal electrode displays significant capacitive retention (~96 %) and notable coulombic efficiency after 10,000 cycles galvanostatic charge/discharge at current density of 10 A/g. The prepared graphene structure with this novel method exhibits remarkable EDLC performances compared to other graphene-based supercapacitors cited in the literature. Owing to their sustainable quality and considerable quantity, these performant supercapacitor electrodes should be beneficial from an industrial vantage point.