Self-regulation is the process of generating new alternative schemas that can be reequilibriated through feedback and accommodation of observed information and the existing disquilibriated schemas. The purpose of this study was to compare neurocognitive thinking processes in two groups based on brain activity data from scientific gifted and general students’ self-regulation process during taking mirror-writing tasks. As a result of the study, the OFC area, where activities appear in the process of performing self-regulating tasks in common with science gifted students, is an area that has the function of predicting errors and determining success or failure. This means that self-regulation is taking place to anticipate the outcome of an action and to continuously check whether it is consistent with the actual results. In addition, comparing brain activity in assimilation, conflict, and accommodation processes that subdivide the process of self-regulation, we found that there were differences between processes and groups. In particular, the DLPFC area, where activities appear during the conflict process and accommodation process that strive to form an alternative schematic, is an area that has the function of manipulating information in the working memory. This means that efforts are being made to reach equilibrium through attempts to integrate information for problem solving and one’s strategy. The findings of this study may be used as relevant data for education that can enhance self-regulation for gifted education for all, while also being as data on neurological methods used as a verification tool to support research in cognitive psychology.