The dynamics of chaos have been widely used in nonlinear science, such as neural networks, extreme event statistics, and the biophysics of chaos self-organization. Superconducting qubits are artificial atoms based on the Josephson junction structure of nonlinear superconducting devices, offering high design flexibility and ease of coupling and control. In this paper, the generation of chaos through the coupling between superconducting qubits and LC resonant circuits is investigated. By varying the ratio of Josephson energy to charge energy, the coupling coefficient, and the energy of the external driving field, the generation and control of chaos within the system are numerically analyzed. This study provides theoretical support for parameter selection ensuring the confidentiality and fidelity of quantum information transmission based on the chaotic dynamics of superconducting qubits.