We theoretically study the properties of the ground state of the parallel-coupled double quantum dots embedded in a mesoscopic ring in the Kondo regime by means of the two-impurity Anderson Hamiltonian. The Hamiltonian is solved by means of the slave-boson mean-field theory. Our results show that in this system, the persistent current depends sensitively on both the parity of this system and the size of the ring. Two dots can be coupled coherently, which is reflected in the giant current peak in the strong coupling regime. This system might be a candidate for future device applications.