Graphene, an extraordinary two-dimensional carbon nanostructure, has attracted global attention due to its remarkable electronic, mechanical and chemical properties. This work reports a novel one-step green and versatile route to produce up to 1 mg/mL of graphene by facile exfoliation of raw graphite in ethanol–water mixtures. This approach is viable due to the predictions of material solubility by exploiting the Hansen Solubility Parameters. The effective surface area of the graphene was estimated to be about 1000 m2/g while Atomic Force Microscopy (AFM) analysis was adopted to evaluate the surface characteristics of the samples, whereby the graphene sheets were found to have an average thickness of below 2 nm. The electrochemical characteristic of the graphene was investigated by cyclic voltammetry tests and amperometric detections of hydrogen peroxide (H2O2), a by-product of most oxidase based enzymatic reactions. The graphene was deposited onto the surface of screen printed carbon electrodes (SPCEs) and the modified electrode was found to demonstrate enhanced electro-catalytic response of more than two-fold compared to unmodified electrodes, while the detection of H2O2 showed excellent stability with a 22 times improvement in sensitivity by optimising the number of deposition layers on the electrode surface.