The Hamiltonian of the mesoscopic inductance coupling circuits with mutual inductance was given by Langrangian function,then it was diagonilized through a unitary operator.The normal ordering form of the unitary operator was obtained by the technique of integration within an ordered product(IWOP),and the quantum fluctuations of charge and its conjugate quantity of this system were discussed. It was found that a rotated two single-mode squeezed vacuum state could be generated by using the system.