A new single-particle equation of the Kohn-Sham-Dirac type is derived from a relativistic current- and spin-density functional theory ( RCSDFT ), and is here applied to the calculations of the atomic structures of the rare-earth elements. Both the relativistic effects and the magnetic effects are taken into account on an equal footing, and the numerical calculation is carried out by modifying the method of Cortona et al. Because of the presence of the effective magnetic field, the degeneracies in all orbits are completely resolved like the Zeeman splittings. Total spin and orbital angular momenta over all the occupied states are shown to agree reasonably well with Hund's rules for the rare-earth ions.