Obtaining an understanding, at the atomic level, of the interaction of nanomaterials with biological systems has recently become an issue of great research interest. Here we report on the molecular dynamics study of the translocation of fullerene C-60 and its derivative C-60(OH)(20) across a model cell membrane (dipalmitoylphosphatidylcholine or DPPC bilayer). The simulation results indicate that, although a pristine C-60 molecule can readily ``jump'' into the bilayer and translocate the membrane within a few milliseconds, the C-60(OH)(20) molecule can barely penetrate the bilayer. Indeed, the mean translocation time via diffusion for the C-60(OH)(20) molecule is several orders of magnitude longer than for the former. It was also determined that the two different forms of fullerenes, when adsorbed into/onto the bilayer, affected the membrane structure differently. This study offers a mechanistic explanation of that difference and for the reduced acute toxicity of functionalized fullerenes.