Computer education plays a very important role in achieving certain general, social and civilization goals-such as educated and creative individuals, people ready for the challenges brought upon them by the information society. This article presents a segment from a broader research of the barriers which emerge in the process of teaching Computer Science in grammar schools. The research was carried out the sample of about 1200 respondents, senior year pupils from several different towns in Vojvodina, and college students who had previously finished grammar school. Based on the analyses of numerous studies and research done in our country and abroad, we have made a classification of barriers in the teaching of Computer Science into pedagogic-psychological and social barriers which can also be classified into one of these categories. This study employed multivariate methods to evaluate the connections between the barriers in the teaching of Computer Science and the school achievement of pupils.