The convergence process has for many decades captured the attention of economists and its importance has especially increased with deepening economic integration. A wide range of indicators is used in the professional literature to establish real and nominal convergence in the European Union, but national competitiveness is usually not among them, despite the fact that national competitiveness has in recent years been an important indicator of economic performance at the national level. Furthermore, converging competitiveness is a necessary precondition for further common development of the European Union. The aim of this contribution is to demonstrate whether the competitiveness of the EU countries is converging or not. Competitiveness is defined as the ability of a country to deliver beyond‑GDP goals to its inhabitants and the indicator of outcome competitiveness is used for its evaluation. We apply methods of beta and sigma convergence and the results of both methods show that while the differences in competitiveness among the EU member states decreased in the period 2003–2012, it did so very slowly.