The structure of the electrical double layer in the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) near a basal plane of graphite was investigated by molecular dynamics simulation. The calculations were performed both for an uncharged graphite surface and for positively and negatively charged ones. It is found that near an uncharged surface the ionic liquid structure differs from its bulk structure and represents a well-ordered region, extending over approximately 20 A from the surface. Three dense layers of ca 5 A thick are clearly observed at the interface, composed of negative ions and positively charged rings. It is established that in the first adsorption layer the imidazolium ring in the [BMIM]+ cation tends to be arranged in parallel to the graphite surface at a distance of 3.5 A. The [PF6]- anion is oriented in such a way that the phosphorus atom is at a distance of 4.1 A from the surface and triplets of fluorine atoms form two planes parallel to the graphite surface. Ions adsorbed at the uncharged surface are arranged in a highly defective 2D hexagonal lattice and the corresponding lattice spacing is approximately four times larger than that of the graphene substrate. The influence of the electrode potential on the distribution of electrolyte ions and their orientation has also been investigated. Increase in the electrode potential induces broadening of the angle distribution of adsorbed rings and a shift of the most probable tilt angle towards bigger values. It was shown that there are no adsorbed anions on the negatively charged surface (sigma = -8.2 microC cm(-2)), but the surface concentration of adsorbed cations on the positively charged surface (sigma = +8.2 microC cm(-2)) has a nonzero value. In addition, the influence of the surface charge (+/- sigma) on the volume charge density and electric potential profiles in an electrolyte was studied. The differences in the cation and anion structure result in the fact that the integral capacitance of the electrical double layer depends on the electrode polarity and equals C = 4.6 microF cm(-2) at sigma = -8.2 microC cm(-2) and C = 3.7 microF cm(-2) at sigma = +8.2 microC cm(-2).