Graphene electrodes are investigated for electrochemical double layer capacitors (EDLCs) with lithium ion electrolyte, the focus being the effect of the pore size distribution (PSD) of electrode with respect to the solvated and desolvated electrolyte ions. Two graphene electrode coatings are examined: a low specific surface area (SSA) xGNP-750 coating and a high SSA coating based on a-MWGO (activated microwave expanded graphene oxide). The study comprises an experimental and a computer modeling part. The experimental part includes fabrication, material characterization and electrochemical testing of an EDLC with xGNP-750 coating electrodes and electrolyte 1M LiPF6 in EC:DMC. The computational part includes simulations of the galvanostatic charge-discharge of each EDLC type, based on a continuum ion transport model taking into account the PSD of electrodes, as well as molecular modeling to determine the parameters of the solvated and desolvated electrolyte ions and their adsorption energies with each type of electrode pore surface material. Predictions, in agreement with the experimental data, yield a specific electrode capacitance of 110 F g−1 for xGNP-750 coating electrodes in electrolyte 1M LiPF6 in EC:DMC, which is three times higher than that of the high SSA a-MWGO coating electrodes in the same lithium ion electrolyte.