The binding structures and electronic states of sodium ion and atom (Na(+) and Na) trapped on the smallest fullerene surface (C(20)) have been investigated by means of density functional theory (DFT) calculation to elucidate the nature of interaction. It was found that the Na(+) ion can bind two sites of C(20): one is on-top site where Na(+) ion binds to the carbon atom of C(20), while the other is a pentagonal site where the Na(+) ion binds to five membered ring of C(20). In case of sodium atom, the similar binding structures were obtained on C(20) surface. The nature of the interaction between Na(+) (Na) and the C(20) cluster was discussed on the basis of theoretical results.