The quantum computation needs to maintain the quantum state coherent and the entanglement,but these two characteristics are very easy to be destructed by the decoherent process,therefore,how to overcome the effect of decoherence is the key to implement quantum computation. The Hamiltonian of the superconducting circuit was derived from circuit graph theory,and multilevel dissipative dynamics was studied by the Bloch-Redfield function. Finally,under two-level approximation,the influence of mutual inductance on the decoherence of the magnetic flux qubit was discovered. And how to change the mutual inductance to reduce the decoherence time of the magnetic flux quantum bit was discussed.