In the present work, the catalytic activity of metal-fullerene C58M (M = Mn, Fe, Co, Ni, and Cu) toward oxygen reduction reaction (ORR) and CO oxidation has been explored by detailed density functional theory calculations. Firstly, the binding energy of various ORR species (OOH, O, and OH) on C58M and the corresponding adsorption structures are calculated. The results show that the adsorption strength of any ORR species on C58M follows the order of C58Mn > C58Fe > C58Co > C58Ni > C58Cu and C58Co shows the closest binding energy compared with the Pt(111) surface. Further analysis of the free energy change of ORR indicates that C58Co, C58Ni, and C58Fe have different degrees of catalytic activities, with the calculated free energy change of rate-determining step of -0.70, -0.32, and -0.04 eV, respectively. On the basis of the above results, the C58Co obviously has the highest ORR activity, with a relatively small overpotential of 0.53 V. In addition, the adsorption free energy of OH can be used as a good descriptor for ORR activity due to the nearly linear relationships between increment G(*OOH), increment G(*O), and increment G(*OH). At last, the catalytic property of C58Co toward CO oxidation reaction is also explored. The calculated results show that CO oxidation on C58Co follows LH mechanism and the rate-determining step is recognized as *CO + *O-2 -> *OOCO, with the energy change of -0.13 eV.