Grand canonical Monte Carlo simulation results are reported for an electric double layer composed of a graphene electrode and spherical ions. The electrode is a honeycomb structured corpuscular carbon with a partial point electric charge immersed at the centre of each carbon atom. Ions are approximated by soft spheres with a point electric charge located at the centre. The soft ion-ion and carbon-ion interactions are describe by the Lennard-Jones (LJ) potential. The diameter of anions is fixed as r(0), = 300 pm (r(0) is the LJ potential parameter) while that of cations, r(0,+), takes the following values: 250, 300, and 350 pm. The ion charge numbers are + 1 and -1, respectively, for cations and anions. Results for the graphene electrode-ion singlet distributions, the mean electrostatic potential and differential capacitance are obtained for the electrolyte concentrations c = 1, 2 and 3 mol/dm(3) and the electrode charge density varying from -0.9 to +0.9 C/m(2) at the relative permittivity 78.5 and temperature 298.15 K. It is found that at the negative electrode charges, with increasing cation diameter the cation singlet distribution maximum is shifted towards greater distances from the electrode and the height of the maximum is elevated. For high negative and positive values of the electrode charges another layer of cations is observed to appear. With increasing an electrolyte concentration the shape of differential capacitance curve changes from that with a minimum surrounded by maxima, through a plateau preceded by a single maximum into that of a distorted bell. (C) 2016 Elsevier Ltd. All rights reserved.