Noncovalent interactions between aromatic compounds and fullerenes have received considerable attention in various fields of science and technology. Employing benzene (C6H6) and C60 fullerene as model molecules, we theoretically explored in the present study the nature of this kind of noncovalent interaction. Our results clearly show that the π···π stacking configurations of the complex C6H6···C60 are more strongly bound than in the C-H···π analogues, and the C-H···π interactions in the C-H···π configurations of C6H6···C60 are not of the hydrogen bonds. According to symmetry adapted perturbation theory analyses, all of the configurations of C6H6···C60 are dominated by dispersion forces. The percentage of the dispersion components in the overall attractive interactions for the π···π stacking configurations is smaller than the percentage of the dispersion components in the overall attractive interactions for the C-H···π configurations, whereas the percentage of the electrostatic terms in the overall attractive interactions for the π···π stacking configurations is larger than the percentage of the electrostatic terms in the overall attractive interactions for the C-H···π configurations. This is distinctly different from the case of the benzene dimer.