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We theoretically investigate properties of the ground state of a closed dot-ring system with a magnetic flux in theKondo regime by means of a tight-banding Anderson Hamiltonian, using the Slave-Boson mean-field approach.The persistent current shows interesting dependences on the parity and on the size of the system. The signatureof Kondo resonance at ξk/L = 0.15 is expected to be observed experimentally in the future. With the intensityof the coupling tD changes from weak to strong, the properties of the system changes largely, which are differentfrom the in-line one because of the attached dot.