Giftedness is a set of features that allow an individual to consistently achieve a remarkable out of the average work done in one or more activities he deals with. Signs of gift manifestation are different, but most often, children who are gifted, solve certain tasks faster and easier than their peers. One authors define giftedness through the qualities of gifted children, others base their definitions on cognitive models of giftedness and the third on achievements. It is important for gifted children to provide them quality support in preschool education and that was inferred from the presentation of the practical part of this work. Educators from kindergarten "Vrapcic" with the boy conducted activities on an individualized program. After the psychological treatment, where the boy was initiated from his educators from kindergarten „Vrapcic“, the boy started to attend a playroom for a potentially gifted children, called „Bistric“. An individualized work plan with a boy was designed and made by educators from kindergarten „Vrapcic“. It is based on boy's interests and needs. The goal of the educators was to encourage additional development of his specific abilities and to work on those segments where he was inferior. The main goal of the playgroup for gifted children is to encourage the full development of potentially gifted children and meeting the basic psychological needs and special educational needs of gifted children according to the principle of individualization.