Attention-deficit/hyperactivity disorder (AD/HD) is a prevalent behavioral disorder particularly in children, but the accurate diagnosis of ADHD is still challenging due to its heterogeneity and comorbidity. Toward a deeper understanding of the pathophysiology of ADHD, we investigated changes in the complexity of EEG recordings in adolescent ADHD patients during cognitive task, compared with that of healthy subjects. EEGs were recorded from 11 male adolescent ADHD patients and 12 age-matched male healthy subjects in a resting condition and during auditory cognitive task. The complexity of the EEGs was estimated by the approximate entropy (ApEn), a nonlinear statistic quantifying an irregularity of a time series. We found that the mean ApEn of ADHD patients was significantly lower than that of healthy subjects in frontal, left parietal and left occipital regions during cognitive tasks, not in a resting condition. Ad hoc analysis revealed that, whereas healthy subjects exhibited a marked increase in the ApEn during cognitive tasks, ADHD patients exhibited no increase in ApEn values due to deficits in the information processing of the cortical network. These results indicate that abnormal cognitive information processing in ADHD patients, such as inattention, hyperactivity and impulsivity, result in less flexible changes in the complexity of the EEG during cognitive-state transition of the brain. We suggest that the ApEn analysis of the EEG during cognitive tasks can provide a possible tool for diagnosing ADHD and assessing the severity of the disease.