Since drowsy driving is a major cause of serious traffic accidents, there is a growing requirement for drowsiness prevention technologies. This study proposes a drowsy driving prediction method based on eye opening time. One issue of using eye opening time is predicting strong drowsiness before the driver actually feels sleepy. Because overlooking potential hazards is one of the causes of traffic accidents and is closely related to driver cognition and drowsiness, this study focuses on eye opening movements during driving. First, this report describes hypotheses concerning drowsiness and eye opening time based on the results of previous studies. It is assumed that the standard deviation of eye opening time (SDEOP) indicates driver drowsiness and the following two transitions are considered: increasing and decreasing SDEOP. To confirm the hypotheses, the relationship between drowsiness and SDEOP was investigated. The two transitions were observed in preliminary experiments on a test course (number of drivers: 7, speed: 80 km/h). A drowsy driving prediction method was then developed based on the hypotheses. The proposed method has upper and lower thresholds, and predicts drowsiness when SDEOP crosses one of the thresholds. The thresholds are determined by an adaptation session to address individual differences in SDEOP. Finally, experiments on the test course (number of drivers: 10, speed: 80 km/h) confirmed that this method has the potential to predict strong drowsiness 5 to 25 minutes in advance.