The magnetic field effects on selective photoionization of the atoms of Lanthanides have been examined in a point of view of the enhancement of the efficiency of selective photoionization. The Zeeman shifts and the hyperfine structures have been calculated by the formulae approximated by LS coupling, and the electronic orbitals by the Hartree-Slater equation. The dependence of the energy levels on the magnetic field has been informed. The photoionization rate due to the polarized lights in a magnetic field has been evaluated. The variation of selection rules of the photoionization due to polarized lights, also, has been informed. (Author).