Introduction: The paper deals with a possible level of risk in cerebrally gifted pupils in relation to bullying at lower secondary schools and grammar schools. In terms of personality characteristics, gifted pupils form a very diverse group, but some research suggests that they might be a risky group concerning school bullying. In the Czech Republic, the most of cerebrally gifted pupils attend ordinary primary schools or grammar schools and they are in daily contact with other pupils. Due to ambiguous research results, there is a question if it is really possible to think of certain risks in the case of cerebrally gifted pupils in relation to their school environment. Quantitative research tried to answer these questions. Methods: The research was focused on the perception of selected areas in the class social environment by the diagnosed cerebrally gifted pupils, the undiagnosed gifted ones and the ordinary pupil population. A quantitative research strategy for bullying incidence mapping in primary and grammar schools were determined. As a research tool, a questionnaire was chosen. Gathered data from the initial questionnaire were evaluated by the following methods: dispersion analysis (ANOVA) for data spread by Gauss curve, Kruskal-Wallis test for data with non-Gauss distribution, arithmetic mean, Pearson Chi-Square Test, correlation analysis and contingency tables. Results: There are differences among the class climate in ordinary classes and the classes with diagnosed cerebrally gifted pupils and undiagnosed pupils. The comparison was at the level of schools, it means among primary schools and grammar schools. It was found out that the cerebrally gifted respondents repeatedly met some form of bullying. Discussion: On the basis of the findings, the authors assumed that cerebrally gifted pupils (GP) represent a risky group in social interaction with their peers and are more prone to different symptoms of bullying. This has not been statistically confirmed. The overall score was similar in other groups. Limitation: The views of teachers and the views of some psychologists suggest that within the GP group, there is a special group of GP that is not identifiable by traditional questionnaires. For further research, it is worthwhile to consider opting for such research methods that could reveal those pupils. Conclusions: Based on these results, it is possible to support those authors who consider GP as a specific group with their own problems, different values and perceptions, but similar to their peers.