The analysis of the current state of the Ukrainian system of engineering education indicates the prevalence of traditional teaching-learning approaches in contrast to the modern needs of the labour market. Many universities across the world use the problem/project-based learning (PBL) which is an effective approach for the development of design and management skills of engineering students. The paper describes a detailed structure of a PBL course in project management and practical experience related to its implementation in an engineering degree programme at Bohdan Khmelnytsky National University of Cherkasy. Also, the results of surveys carried out in order to study the students' generic competences' development and perception of the PBL process are presented. The results show that students understand the diversity of PBL aspects and the influence of the PBL approach on their professional characteristics such as teamwork, ability of self-directed learning, communication and problem-solving skills.