We have investigated the ground state and the two lowest excited states of the CeF molecule using four-component relativistic multiconfigurational quasidegenerate perturbation theory calculations, assuming the reduced frozen-core approximation. The ground state is found to be (4f(1))(5d(1))(6s(1)), with Omega = 3.5, where Omega is the total electronic angular momentum around the molecular axis. The lowest excited state with Omega = 4.5 is calculated to be 0.104 eV above the ground state and corresponds to the state experimentally found at 0.087 eV. The second lowest excited state is experimentally found at 0.186 eV above the ground state, with Omega = 3.5 based on ligand field theory calculations. The corresponding state having Omega = 3.5 is calculated to be 0.314 eV above the ground state. Around this state, we also have the state with Omega = 4.5. The spectroscopic constants R(e), omega(e), and nu(1-0) calculated for the ground and first excited states are in almost perfect agreement with the experimental values. The characteristics of the CeF ground state are discussed, making comparison with the LaF(+) and LaF molecules. We denote the d- and f-like polarization functions as d(*) and f(*). The chemical bond of CeF is constructed via {Ce(3.6+)(5p(6)d(*0.3)f(*0.1))F(0.6-)(2p(5.6))}(3+) formation, which causes the three valence electrons to be localized at Ce(3.6+).