The article is devoted to a model of group mentoring in work with gifted children, which is considered to be a way of transferring knowledge, skills, and abilities from a more experienced and knowledgeable specialist to a young person, providing young people with support in socialization and growing up. The article presents many years of experience of using network research projects organized by the Association of Teachers Working with Gifted Children. The article identifies the conditions necessary for the organization of a network research project. The functions of teachers participating in projects as tutors are described. The formats of network project organization are indicated: game, business project, research, quest, etc. The authors consider examples of some network projects in the form of an organizational activity game and business project. The effectiveness of network research projects as a form of group mentoring has been identified based on expert assessments of skills development changes among gifted students. Skills, on the development of which the work in network projects focuses, are information skills (the ability to search for information, master modern information and communications technology, etc.), communicative skills (the ability to interact productively), team- building skills (the ability to work in groups with both permanent and changing members, etc.), and skills of presenting scientific ideas (the ability to visualize, describe, and present projects).