The "proving process" was considered as the stages that should be exist in a proof and in this study, it was aimed to investigate the mathematical proving processes and opinions about proof of gifted students. Case study, one of the qualitative research methods, was used in the study. The research was carried out with the students determined by criterion sampling method. The attendance of students to Science and Art Education Centre, the data obtained from the Proof Interview Form and the opinions of mathematics teachers constituted the criteria of the criterion sampling method. As a data collection tool, the Proof Interview Form and the Proof Clinical Interview Form were used. "Proof Clinical Interview Form" prepared by the researcher was applied to examine the students' proving processes. The data obtained from the clinical interviews were analysed with the descriptive analysis. Students were generally able to examine the problem situation and formulate the conjecture, but they did not determine the appropriate strategies, perform the necessary actions and summarize clearly while proving.