The article reviews the problems of intercultural competence (ICC) in Western and Russian psychology. Special attention is given to considering the correlation between personality characteristics and intercultural competence using the example of Big Five factors. The results of empirical research of correlations between the indicators of intercultural competence and the Big Five factors in students are presented. For the diagnosis we used «The Scale of intercultural sensitivity» proposed by O. E. Khuhlaev and M. Y. Chibisova and «The Five Factors questionnaire» in M. V. Bodunov and S. D.