Drowsiness is an awake state with increased sleep drive, yet the neural correlates and underlying mechanisms remains unclear. Here, we established a mouse model of drowsiness, where mice are fasted for 1 day and then allowed to overeat high-fat food (to promote sleep) while positioned in an open-field box (to promote vigilance). They fall into a long-lasting drowsy state, as reflected by repeated and open-eyed nodding of the head while in a standing position. Simultaneous recording of electroencephalogram (EEG) and neck electromyogram (EMG) readouts revealed that this drowsy state including nodding state had multiple stages in terms of the relationship between the level of vigilance and head movement: delta oscillations decreased in power prior to the head-nodding period and increased during the non-nodding period. Cav3.1-knockout mice, which have reduced delta oscillations, showed frequent head nodding with reduced duration of nodding episodes compared to wild-type mice. This suggests that the balance of drive is tilted in favor of wakefulness, likely due to their previously proposed decrease in sleep-promoting functions. Our findings indicate that delta oscillations play a dominant role in controlling vigilance dynamics during sleep/wake competition and that our novel mouse model may be useful for studying drowsiness and related neurological disorders.