Using the slave-boson mean-field approximation, we theoretically study the transport properties of the ground state of the T-shaped coupled quantum dots with two metallic leads by means of one-impurity Anderson Hamiltonian. It is found that when this system is in the equilibrium state, with the increase of the inter-dot coupling, the Kondo resonance is suppressed, and the single Kondo peak of the density of the Kondo quantum dot is split into two asymmetric Kondo peaks. When it is in the non-equilibrium state, when increasing the bias, this asymmetric Kondo splitting is enhanced.