Using an equation of motion technique, we investigate the Kondo effect in a quantum dot coupled to ferromagnetic leads and a mesoscopic ring. It is shown that the Kondo resonance at the Fermi level of the dot presents the periodic change along with the aggrandizement of the magnetic flux and the number of lattice sites NR in the mesoscopic ring, and for the antiparallel spin alignment the Kondo resonances for spin-up and spin-down configurations appear at the same position. However, for the parallel spin alignment, the Kondo resonance splits for the spin-up and spin-down configurations.