Cognitive deficits in depression are mostly apparent in executive functions, especially when integration of information and reasoning is required. In parallel, there are also numerous studies pointing to the frontal alpha band asymmetry as a psychophysiological marker of depression. In this study, we explored the role of frontal alpha asymmetry as a potential factor explaining the cognitive problems accompanying depression. Twenty-six depressed and 26 control participants completed a reasoning task and underwent 5 minutes of electroencephalography recording. In line with the previous studies, depressed people showed difficulties with reasoning but we did not observe the relationship between frontal asymmetry in the alpha band and depression. However, we found that in the depressed group the frontal alpha asymmetry index was characterised by larger variance than in the control group, and it was also a strong predictor of cognitive functioning exclusively in the depressed group. Our results point to the disruption of a psychophysiological balance, reflected in changed frontal alpha asymmetry (into more left-sided frontal asymmetry in the alpha band, reflecting more right-sided cortical activity) as a possible brain correlate of cognitive disturbances present in depressive disorders.