The scientific discipline of project management is gaining in importance every day and it is developing new techniques, methodologies and competences for successful project management. A specific form of projects - startup projects, have proven to be important for the development of entrepreneurship and the national economy. Startup projects develop innovations and launch them into the market under uncertain conditions, which causes a high rate of startup failures. For startup projects to be more successful and increase their chances of success - techniques, competences and project management methodology must be applied. The main source of generally accepted project management competences in this paper is the IPMA's standard ICB4. It is explored what project management competences are most important for the success of startup projects, according to the opinions of leaders and members of the startup teams. A quantitative survey was conducted through questionnaires. Descriptive analysis of the results showed that the majority of respondents consider competences in the People domain as the most important for the success of a startup project. The opinions of leaders and team members generally agree on importance of individual competences in each domain. The results imply that for a successful startup project people in the project team should develop competences: personal integrity and reliability, relations and engagement, leadership, teamwork, project design, change and transformation, strategy, culture and values, and power and interest.