In recent years in psychological and pedagogical sciences there is a trend for increase of interest in studies of students' potential in higher education institutions, because it is the major factor affecting development of student's inner potential. Majority of works in this field deal with the issues of study of student's personal potential, however the problem of leadership potential development in students (i.e. the question of development of leadership qualities directly within education space of a pedagogical university) is understudied, especially concerning students of pedagogical departments. Theoretical and methodological basis of the research is the analysis of psychological and pedagogical understanding of leadership as a phenomenon of development of leadership skills in students. The article contains the results of the theoretical analysis of leadership potential development in student's personality within education space of a pedagogical university, define the structure of student's leadership potential, study the content of the process of leadership potential development within education space of a pedagogical university. The study describes conditions for effective development of leadership skills.