In the Born-Markov approximation and two-level approximation, and using the Bloch-Redfield equation, the decoherence property of superconducting quantum circuit with a flux qubit is investigated. The influence on decoherence of the mutual inductance coupling between the circuit components is complicated. The mutual inductance coupling between different loops will decrease the decoherence time. However, the mutual inductance coupling of the same loop, in a certain interval, will increase the decoherence time. Therefore, we can control the decoherence time by changing the mutual inductance parameters such as the strength and direction of coupling.