The study of foreign competence at the present stage of the higher education development becomes more relevant. The article emphasizes the organizational-pedagogical conditions, providing the formation of foreign competence in students with the features of linguistic giftedness. The way to reveal the students, who have the features of linguistic giftedness, is presented. Experimental teaching showed the increased level of independent behavior in the process of foreign language study; the work in small groups on solution of linguistic tasks to the fullest extent actualizes potential linguistic abilities of students; the satisfaction with the learning process of subject "Foreign Language" has also increased.