Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finitedifference Schrodinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved.The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrodinger equation can be divided into two Mathieu equations in p representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.