A five-state modified BEG model is proposed for describing aqueous electrolyte in cylindrical pore so narrow that only one row of particles can be stationed. Two properties the closest to the actual situation of the aqueous electrolyte are integrated into the model: cation is dimer comprised of two tangentially tethered hard spheres of different diameters: one is charged, while the other is neutral, and solvent is modeled as neutral hard sphere with an electric dipole. The system partition function is obtained by numerically solving maximum real root of characteristic equation of Kramers-Wannier transfer matrix. The present theory reduces to that by the Rochester et al by making both the cation neutral sphere size and electric dipole moment of the solvent equal to zero. The model is used to investigate effects of cation shape and electric valence, solvent electric dipole moment, and cylindrical pore radius on specific differential capacitance and specific energy storage in electric double layer supercapacitor formed inside the cylindrical pore. Main findings are briefly described below. (i) With dimer counter-ion electric valence changing from 1 to 2, the peak becomes higher, and the peak position becomes nearer to the zero charge potential; as a comprehensive effect of these changes, the dimer counter-ion electric valence does not exert obvious influence on the saturation value , but reduces the threshold electrode potential strength , beyond which the value is just and approximately reached. (ii) Whether the dimer counter-ion is monovalent or bivalent, the peak height and the value tend to rise with the dimer neutral site size decreasing, but influence of the value on the value is very small. Only when the value is small enough, the value rises a little with decrease of the value. (iii) Increase of solvent electric dipole moment (wheth