Following the methodology of existential pedagogy, we believe that a person's upbringing should proceed, first of all, from his understanding of freedom, a desire to become what he represents himself, therefore, the most important component of the process of upbringing a free person is the pedagogical support of his self-development. The article reveals the pedagogical possibilities of additional education for children in the formation of a self-developing personality of a child, shows the conditions for creating a subject-oriented educational environment, which consists in ensuring the possibility of developing and implementing an interesting self-development project for students, eventfulness of the educational process, ensuring the formation of a need for self-development through the creation of problem situations associated with the need to overcome, purposeful and systematic use in the educational process of methods and techniques aimed at the formation of moral value orientations. The conditions are disclosed on the example of describing some aspects of the educational activities of the Galaktika Children's and Youth Center for Space Education in the city of Kaluga, the Constellation Center for the Development of Children and Youth Creativity in the city of Kaluga and the Regional Ecological and Biological Center of Students. The article proposes the author's methodology «My ideal», aimed at studying the image of «I-ideal» adolescents aged 11 to 14 years, developed in the context of a reflexive-value approach to pedagogical support of self-development of adolescents in additional education. The article presents the results of an empirical study of the experience of pedagogical support for self-development of adolescents in the system of additional education (on the example of the city of Kaluga), which showed that educational practices of the development of value-semantic and reflexive-regulatory spheres of a teenager's personality have been accumulated in institutions today. Along with this, it is necessary to systematically and technologically approach the implementation of pedagogical support for self-development of adolescents in additional education, aimed at forming the readiness of pupils for existential choice, independent creation and responsible implementation of the project of their own life.