We report the effects of an electric field E on the spin orientations of nickelocene (Nc) deposited on the Cu surfaces by means of first-principles calculations. We employ the Hubbard-U corrected van der Waals density functional to take into account the strong correlation effects of the localized 3d electrons and the non-covalent binding involved in the molecule-surface coupling. We show that the deposited Nc molecule can switch between in-plane (in small E-field) and perpendicular magnetization (in large E-field). We find that the significant charge transfer between the molecule and the metallic surface plays a dominant role in the spin reorientation transition. From an electronic structure perspective, the shift in the Fermi level enhances the coupling between the occupied and unoccupied Ni-3d states of different spin states, which tends to facilitate the perpendicular magnetic anisotropy. These findings shed some light on the electrical control of the magnetic anisotropies of single-molecule magnets on metal surfaces.