The paper deals with the problem of teamwork skills development among students during graph- and-project-based learning. Team solution of graph project task enhances learning and cognitive activity of students. When collaborating in a team, students get involved in the learning process and become its interacting players. The study highlights the personal qualities of students needed for successful team building. The author devises a technique for developing teamwork skills when solving graph project tasks that helps manage, assess, and modify this process, measure the degree of development of the multi-faceted qualities of each team member necessary for harmonious teamwork. The effectiveness should be identified by not the maximum development rate of team-building skills but their minimum indicators. Such an approach makes it possible to avoid the failures in training university graduates and allows students master the necessary skills to build a successful career in the future.