The electronic structure of the GdF molecule is investigated using all-electron Dirac-Fock-Roothaan calculations. It is found that, in the ground state, the Gd atom transfers a 5d electron to the 2p spinors of the F atom, so that the molecule is ionic, having the configuration of Gd+F-. However, the molecule is not purely ionic, since the electrostatic field produced by Gd+ and F- causes the spinor energies of F 2s and one of the Gd 5p to be almost energetically degenerate so that these spinors strongly mix with each other and form covalent bonds. The electrostatic field also causes a large energy lowering for one of the 4f spinors, giving further stability to GdF. The 4f electrons of Gd should be regarded as valence electrons. The lower excited states and positively and negatively ionized states are found to be roughly described by Gd atomlike excitations, ionization, and electron attachments.