Interaction of fullerenes with asymmetric and curved DOPC/DOPS bicelles is studied by means of coarse-grained molecular dynamics simulations. The effects caused by asymmetric lipid composition of the membrane leaflets and the curvature of the membrane are analyzed. It is shown that the aggregates of fullerenes prefer to penetrate into the membrane in the regions of the moderately positive mean curvature. Upon penetration into the hydrophobic core of the membrane fullerenes avoid the regions of the extreme positive or the negative curvature. Fullerenes increase the ordering of lipid tails, which are in direct contact with them, but do not influence other lipids significantly. Our data suggest that the effects of the membrane curvature should be taken into account in the studies concerning permeability of the membranes to fullerenes and fullerene-based drug delivery systems.