The paper is devoted to the problem of creating a system of training of future teachers for work with gifted schoolchildren in mathematics. The authors analyze the existing curricula and basic professional educational programs for the preparation of Bachelors in the directions of training "Pedagogical Education" and "Mathematics and Computer Science" in terms of ensuring the professional competencies of future teachers for the work in the conditions of existence of a professional standard. The authors propose a technology for preparation of students, involved the production of Bachelors with high competencies in the field of working with gifted children in mathematics. The purpose of the article is to analyze the actual level of Bachelor's training for working with gifted children in mathematics and, on this basis, to present the developed system of training future teachers for work with gifted schoolchildren in mathematics. The research methodology is based on a system of basic principles, methods and concepts of the psychological-pedagogical theory of mathematical giftedness: the content analysis of curricula and basic professional educational programs for Bachelor's training, a test for determining the readiness of a teacher to work with gifted children, a test for determining the propensity of a teacher to work with gifted children. The authors have developed and proposed a structure of vocational training of students to work with mathematically gifted children. Some shortcomings in the professional training of future teachers are revealed. The results of experimental work on the improvement of the basic professional educational program in the training directions "Pedagogical education" and "Mathematics and computer sciences" are presented. The existing problem of the lack of competencies of future teachers should be compensated with the help of development of means, techniques, technologies and methods that contribute to the competence of students in working with gifted children in mathematics.