As a model of shale, one part of polycyclic aromatic ring was used to represent the kerogen surface with the structural heterogeneity. The adsorption mechanisms of methane on the surface of the kerogen were investigated by M06-2x functional with D3 dispersion correction. Nine stable adsorption sites and the orientations of methane (CH4) on the surface of the kerogen were systematically considered. Information from different methods lead to the same conclusion that methane prefers to be adsorbed on the sites directly above the carbon atoms of the kerogen rather than above the center of the six-membered rings. The interactions between methane and the surface of the kerogen are the van der Waals interactions. The interaction energies with the basis set superposition error (BSSE) corrections are around 14 kJ mol(-1) at the M06-2x-D3/Jun-cc-pVDZ level. The RDG scatter graphs and the RDG gradient isosurface further illustrate that the interactions between methane and the surface of the kerogen belong to the van der Waals interactions. The weak interactions indicate that the adsorption of methane on the surface of the kerogen is physical adsorption and it slightly depends upon the adsorption sites on kerogen as well as the orientations of methane. These results are helpful for the understanding of the microcosmic mechanism of methane-shale interactions and for the exploitation of shale gas. (C) 2016 Elsevier B.V. All rights reserved.