This paper proposes an estimation method for a driver's drowsiness that uses an identified driver model. In the previous report, it was shown that a driver's involuntary response to a car's motion can be extracted by pre-filtering and provided to the real-time identification method. The identified driver model contains meaningful parameters related to the driver's characteristics. In the present research, the correlation between the identified driver model and drowsiness was investigated using the results of an actual driving test. Then, the drowsiness-estimation function was constructed which evaluated the delay, gain, uncertainties, and time variation of the steering behaviour of the identified driver model. The driving test showed that the proposed method had sufficient precision to provide a warning of inattentive driving.