The preparation of high-fidelity quantum state is a basic requirement for precise control of quantum system. In this paper, by using superadiabatic technology and introducing an auxiliary field strength parameter, we investigate the problem of high-fidelity superadiabatic quantum driving in the Demkov-Kunike model, and discuss the influence of the auxiliary field strength parameters, chirp parameters, coupling strength and static detuning parameters on the adiabatic process of the Demkov-Kunike model. The results show that the fidelity of the system is closely related to the auxiliary field strength parameters. When the appropriate auxiliary field parameters are selected, the system has good parametric robustness, no matter the system is at no static detuning case or static detuning case. The oscillation of transition probability can be suppressed in all parameter ranges. The system can achieve high-fidelity, fast, and superadiabatic quantum driving.