Shared control scheme improves the driving performance while having an impact on driver behavior, drivers would constantly adapt their steering behavior mechanism in interaction with a shared controller. This paper proposes a novel data-driven model-based shared control strategy which is capable of considering drivers’ adaptive behaviors in driver-automation interaction to improve safety. The Koopman operator theory, which is a pure data-driven modeling technology, is adopted to yield an explicit control-oriented driver-vehicle model for shared controller design. Besides, a weighted online extended dynamic mode decomposition (WOEDMD) algorithm is proposed to update the Koopman driver model online for better capturing the driver’s adaptive behavior in driver-automation interaction, which settles the problem of driver’s potential behavior mechanism variations in practice. Based on the Koopman driver-vehicle model, a model-based shared controller is proposed in the model predictive control (MPC) framework, and the potential fields are incorporated in the optimization objectives to ensure safety. A group of human-in-the-loop experiments are conducted on a driving simulator to demonstrate the effectiveness of the modeling and shared control methods. The results show that the Koopman operator theory can be exploited for modeling the dynamics of the driver-vehicle integrated system, and the drivers’ adaptive behavior can be captured by the WOEDMD algorithm. Moreover, the shared controller considering the driver’s adaptive behavior improves the driving safety in the collision avoidance task.