The article is devoted to the problem of professional competence formation in the specialists' training process at the university in contemporary socio-economic and socio-cultural conditions originating in the Republic of Kazakhstan. The emphasis is laid on new scientific and pedagogical approaches to its solution. Special attention is paid to the issue of professional competence formation in extracurricular activity, especially, during job training: approaches' specification to the job training organization and conduction, the development of results' forecasting skills in students, the strategy elaboration for solving both educational and practical tasks. The analysis of domestic and foreign literature is performed on the research problem. In general, it shows that the relevance of this problem is determined not only by social order, but also by the student's needs in self-determination and self-expression. Special attention of foreign and domestic researchers indicates a lack of knowledge on the problem of specialists' professional competence in the university training process, and contradictions between educational institutions' need in competent specialists and their insufficient theoretical and practical training. The developed system of professional competence formation in future specialists consists of four components: target, activity, informative and effective, which allow considering the students' professional practice as the most important element in the highly qualified specialists' training.