Anxiety has commonly been regarded as one of the most significant affective obstacles in language learning achievement, and has been the subject matter of many second language researches (MacIntyre & Gregersen, 2012; Huang, 2012; Hewitt & Stefenson, 2011; Riasati, 2011; Horwitz, 2001). The primary purpose of the present study is to explore the anxiety levels of a class of students studying at the University of Dunaujv aros and to investigate their attitude towards acquiring a second/foreign language. On the basis of the information gained the study is aiming at revealing some degree of correlation between students' anxiety and their academic achievement. Responses to the Foreign Language Anxiety Scale show that the relatively high levels of anxiety among these participants are related to the worry about (1) the consequences of failing their foreign language class, (2) thinking that the others are better at languages and (3) communication with native speakers of the foreign language. However, the results on the relationship between anxiety levels and academic achievements show no significant correlation between these two variables, which leads us to the conclusion that the participants' anxiety levels do not exceed the level which would have a negative impact on their academic results.