The aim of the study was to investigate the relationship between personality structure and brain activity of individuals while resting with eyes closed. In the experiment 110 individuals participated (55 males and 55 females). They were clustered into 5 personality types according to the dimensions of general and emotional intelligence, and the five-factor personality model (FFM) -- extraversion (E), neuroticism (N), openness (O), conscientiousness (C) and agreeableness (A). The resting EEG of individuals was analyzed using three methods: a Fast Fourier Transformation (FFT); Approximated entropy (ApEn), and a low resolution brain electromagnetic tomography (LORETA). The results show that most robust differences between personality types were observed in the gamma band, between types with extreme constellations of dimensions (neurotic type - low emotional intelligence and A; high N), or between types with specific combinations of dimensions (introverts with high IQ, versus extraverts with low to average IQ). These differences were also gender specific. In the gamma band females with different personality structures differed much more than did males, whereas in the lower-1 alpha band a reverse pattern was observed. It was further shown that the differences were much more pronounced in the parieto-occipital brain areas than in the frontal areas.