The concept of intercultural education should be aimed at better understanding of ourselves and others, discovering similarities and differences, recognizing preconceptions, and cooperation in accomplishing our common goals. Intercultural education can be very useful in resolving the issues that arise when different groups live together. Also, intercultural education may benefit the process of getting to know and better understand other cultures and the development of successful communication between cultures. Music courses in grammar schools may contribute to students' intercultural education, because music is an area in which cultural competence can develop significantly. During the December of 2014, for the purposes of this paper, a research study was conducted in a Croatian general programme grammar school. The goal of the study was to determine the students' attitudes toward interculturalism, their attitudes on music courses with regard to interculturalism, and are there any differences in the attitudes and intercultural awareness between first grade students and fourth grade students at the grammar school. A survey questionnaire was used to conduct an anonymous survey among first and fourth grade students. The results of the study have shown that both the first and fourth grade students are aware that they are living in a multicultural environment, as well as that there are examples of certain forms of intolerance towards members of other cultures who share their living surroundings. When compared to fourth grade students, first grade students generally have more positive attitudes toward interculturalism. According to the students' opinions, music courses at the grammar school could be more focused on getting to know the music and musical traditions of the people from other continents. Complementing the syllabus with music from different cultures and from all the continents would contribute to the development of more positive students' attitudes toward interculturalism and help with the realization of goals set by the premise of intercultural education.