Intercultural competence (ICC) is one of the recognized means of preventing and solving intercultural conflicts in the modern global world. ICC conceptualization and diagnostics, as well as opportunities for its development and formation are important subject for scientific discussion in Education, Psychology, Intercultural Communication, etc. The Developmental Model of Intercultural Sensitivity (DMIS) by M.J.Bennett is one of the most applied ICC models in modern psychology. Russian psychologists O.E. Khukhlaev and M.Y. Chibisova developed a Russian-language technique "Intercultural Sensitivity Scale" for ICC diagnostics based on the DMIS, that includes 4 subscales: Minimization, Absolutization, Ambivalence, Acceptance. The analysis of the published data revealed that the Five-Factor Model (FFM) personality traits (neuroticism, extraversion, openness, agreeableness and conscientiousness) are often considered in connection with ICC in Western psychological studies. We believe that the study of FFM personality traits in relation to the DMIS orientations could improve psychological programs aimed at the ICC development in Russian university and school students. The purpose of present research is to show that FFM personality traits can determine the severity of ICC features in Russian university and secondary school students. The sample includes 510 people (63% female): 388 university and 122 school students. ICC was measured with the author's modification of Intercultural Sensitivity Scale by O.Khuhlaev and M.Chibisova, which successfully passed a psychometric testing. The FFM personality traits were measured with the Russian NEO Five-Factor Inventory adaptation by S. Biryukov and M. Bodunov. The descriptive statistics methods, coefficients Cronbach' a and McDonald's., and the multiple regression analysis were used for statistical analysis. Statistical processing was carried out in the R software environment for statistical computing and graphics, version 3.3.2. Findings of our research showed that FFM personality traits affect all the measured ICC subscales, although their impact is not as great as expected (only from 3.6 to 9.5% explained variance). In most cases the FFM personality traits have a different impact on the ICC features in school and university students, wherein relatively universal ICC predictor in both groups is consciousness. Important prospects for our future research are related to, on the one hand, study of other ICC predictors (social attitudes, intelligence level, creativity, etc), and on the other hand, development of the programs to improve the ICC in students in a multicultural educational environment, taking into account their personality features.