Baseline electroencephalogram (EEG) data were collected from twenty-nine 4-year-old children who also completed batteries of representational theory-of-mind (RTM) tasks and executive functioning (EF) tasks. Neural sources of children's EEG alpha (6-9 Hz) were estimated and analyzed to determine whether individual differences in regional EEG alpha activity predicted children's RTM performance, while statistically controlling for children's age and EF skills. Results showed that individual differences in EEG alpha activity localized to the dorsal medial prefrontal cortex (dMPFC) and the right temporal-parietal juncture (rTPJ) were positively associated with children's RTM performance. These findings suggest that the maturation of dMPFC and rTPJ is a critical constituent of preschoolers' explicit theory-of-mind development.