In this paper, we studied the equilibrium geometries, the electronic structures and the binding energies of fullerene C32 as well as its hydrogenates and fluorides interactions by the SCF Hartree-Fock calculations using the latest version of GAMESS of ab initio programs. The fullerene C32 is found to have a 1A2' closed-shell ground state in D3d symmetry or a 1EU singlet state in D3h symmetry. It is predicted to be easy to add some hydrogen or fluorine atoms to the C32 cage and to produce a series of derivatives C32H2n,C32F2n (n=l, 3, 6), in which C32H2,C32F2 (D3d), C32H6a,C32F6c(D3h) are more stable. We suggest that this implies that the vertex of triplet pentagons of the C32 cage is an activation site for addition.