This work is a study about the Adults and Youth Education (Educação de Jovens e Adultos –EJA) in an evening high school equivalency program. We have chosen one school that is part of this kind of program and we have tried to understand its functioning under a critic multiculturalism perspective in an interculturallity vision. Starting with this premise, a qualitative research was carried out, in fact a case study, in a public school of the state of Rio de Janeiro, named Colégio Arpoador. The methodological strategies included, besides the bibliography review, three data collection techniques: observation, documental analyses and semi-structured interview. The main objectives were to analyze if Colégio Arpoador’s teachers recognize and work with the heterogeneous reality of its students, considering their pedagogical practices, the curriculum and the identity construction, besides identifying the contributions of an intercultural education for this kind of equivalency program. The results obtained from the teacher testimonies indicate that they recognize the existence of a great cultural diversity among students, although this reality seems not to constitute a reference to their pedagogical practices and the curriculum subject selection. It seems that teachers don’t experience the intercultural education as a practice, but there is an effort to understand how it works and how it can be stimulated in daily school. From the results, the research tried to show the difficulties found in high school EJA, and also tried to suggest ways to renovate the pedagogical practices, starting from the principle that intercultural education is a very productive way of giving multiples benefits for that reality.