The effect of partial sleep deprivation on cognitive control was studied in 26 students with different levels of trait anxiety. The synchronization–desynchronization reactions of the EEG α-oscillations were evaluated during the Go/NoGo test. In less anxious students, a reduction in sleep time on the night before the study led to a decrease in the desynchronization response to a positive conditioning stimulus (Go) and thus smoothed out the differences with the response to a stimulus that inhibited the behavioral response (NoGo). The smoothing of the α-rhythm responses to stimuli of different signal significance after deprivation indicated deterioration of cognitive control in this group. In students with a high level of anxiety, there were no differences in responses to Go/No Go stimuli either after a night’s sleep of normal duration or after a single sharp reduction of it. They probably had a reduced level of cognitive control, and it did not depend on partial sleep deprivation.