Electric double layer capacitors (EDLCs) have been known as energy storage device and different materials have been used as EDLC electrode materials. Recently, graphene has been considered as one of the most promising materials for use in EDLC structure. In this research, a theoretical study on bilayer graphene (as an EDLC with vacuum dielectric) in two symmetries (D2h and D6h) with different distances and applied voltages is done, where the charge separation among a bilayer graphene structure is calculated by electron deformation orbital theory. Although it was found that capacitance is almost independent of applied voltage in constant distances, the relationship between capacitance and inverse of distance was nonlinear in the cases of constant voltages. The structure change from D2h to D6h did not affect the specific capacitances, significantly, although the areal capacitance of D2h structure was greater than that of D6h structure.