The relevance of the study is determined by the insufficient development of theoretical, content-technological and methodological aspects academic training part-time students through e-learning (Avdeyuk, 2011; Mozhaeva, 2013; Babanskaya, Mozhaeva, Serbin, & Feshchenko, 2015; Ignatova, 2017). The purpose of the article is to develop a structural and functional model of pedagogical support for the part-time post-graduate training via the e-learning. The basis of the strategy in constructing the structural and functional model of pedagogical support of academic training for the part-time post-graduate training via the Moodle system was the competency-based approach. The leading research method for this problem is pedagogical modeling. The article presents a structural and functional model of organizational and pedagogical support of the preparatory course for part-time post-graduates in the Moodle system, which includes target, content, functional and assessment components and reveals their particular characteristics.The article surveys the experience of the Institute of Psychology and Education at Kazan Federal University, Kazan, Russian Federation. The result of testing the structural and functional model of pedagogical support for the part-time post-graduate training via e-learning is the Designing a Preschool Organization Brand electronic course designed by the authors using the Learning Management System (LMS) Moodle (Modular Object-Oriented Dynamic Learning Environment). The model is aimed at adapting post-graduates - the future managers of preschool organizations - to the new conditions of professional activity in the era of global digitalization of education. The results of the study can be applied in training full-time and part-time undergraduate and postgraduate students to obtain a degree in various majors and specialties at a teacher-training university.