The development of intercultural competence (ICC) is important for the modern personality in an unstable and diverse world, but there is a lack of research on this phenomenon in the context of age, gender and intellectual differences. The purpose of the present exploratory study is to identify relations between ICC, cognitive abilities and academic achievements among Russian school students. The sample included 106 (55% female) students in the 9th grade of Moscow secondary school. ICC was measured with the author's modification of "The Intercultural Sensitivity Scale" by Khuhlaev and Chibisova, developed on the basis of the Developmental Model of Intercultural Sensitivity by Bennett. Cognitive abilities were determined with the "School Test of Intellectual Development" by Akimova et al. Academic achievements were evaluated using GPA. The findings of our research show that: (1) higher academic achievements and cognitive abilities usually characterize schoolchildren, who are not inclined to absolutize cultural differences and do not consider them to be barriers to intercultural interaction; (2) the most significant predictors of ICC features from the studied cognitive abilities are "analogy" and "generalization," but "generalization" has opposite impacts in male and female students. This fact should be taken into account in the context of ICC developments, especially in male school students prone to ethnocentrism.