The molecular geometries and electronic structures of the fullerene derivatives C36(OH)n (n = 1～2) have been investigated on the basis of density functional theory calculation at the B3LYP/6-31++G* level. The geometry optimization results indicate that the location of C2 atom is the most active site in the three potential adding patterns, and the C1 or C2 site has a larger binding energy than C3 for the addition reactions of C36 (D6h) cage and OH radicals resulting from the larger curvature. The electronic structure calculation results disclose that the C2 site has larger electronic population in HOMO and larger spin density, and the addition reaction on the C2 site need overcome a lesser energy gap than that on the C1 or C3 site. Thus, the addition is controlled jointly by the curvature and the electronic factors. Besides, when two hydroxyls are added to the C36 surface, the C2 sites are also the most active locations. The most stable addition adduct of C36(OH)2 is the isomer which holds Ci symmetry, and the spin multiplicity seriously affects the stabilities of the adducts.