In this work, we investigate the potential of a novel carbon composite as an electrode for high-voltage electrochemical double-layer capacitors. The carbon composite was prepared following a sustainable synthetic approach that first involved the pyrolysis and then the activation of a precursor formed by winery wastes and graphene oxide. The composite prepared in this way shows a very high specific surface area (2467 m²·g⁻¹) and an optimum pore size distribution for their use in supercapacitor electrodes. Graphene-biowaste-derived carbon composites are tested as active electrode materials in two different non-aqueous electrolytes, the ammonium salt-based conventional organic electrolyte and one imidazolium-based ionic liquid (1 M Et₄NBF₄/ACN and EMINTFSI). It was found that the presence of graphene oxide led to significant morphological and textural changes, which result in high-energy and power densities of ~27 W·h·kg⁻¹ at 13,026 W·kg⁻¹. Moreover, the devices assembled retain above 70% of the initial capacitance after 6000 cycles in the case of the organic electrolyte.