Organic batteries are promising alternatives to the present rechargeable battery technologies, mainly due to projected lower fabrication costs, less environmental impact, more versatility, and chemical and mechanical flexibility. In this study we investigate potential organic battery electrodes composed of an electronically conductive graphene monolayer functionalized with redox-active anthraquinone (AQ). The combination overcomes common drawbacks of organic batteries: (i) the solubility of the organic redox-active materials in the electrolyte is mitigated by anchoring onto graphene and (ii) the need for a large amount of conductive additives in the composite electrode is circumvented by the high conductivity of graphene. The electrodes are modelled by various density functional theory (DFT) based approaches and their fundamental promise as part of Li, Ca, and Al based batteries are outlined. We model the design of the electrodes, such as AQ attachment and loading, the thermodynamics of accepting mono to trivalent ideal charge carriers from the electrolyte, i.e. Li⁺, Ca²⁺, and Al³⁺, and the kinetics of ion diffusion at the electrode surface by assessment of the activation barriers. From the calculated multi-step electrode potential profiles, the theoretical electrode energy densities, with respect to the redox-active part, are 570 and 512 W h kg⁻¹ for Li and Ca, respectively, which is quite comparable to the active materials of inorganic medium voltage lithium-ion battery electrodes. As the average potentials are in the range 0.5–1.2 V vs. Mⁿ⁺/M⁰ these materials are either to be used as negative electrodes, combined with a high or medium potential positive electrode, or as positive electrodes vs. metal electrodes, for low voltage battery application.