Maintaining the EU's position in the world is preconditioned (among other things) by sustainable economic growth in its member states. Currently, all the EU countries are facing the effects from the rapidly aging population, which is one of the most serious obstacles to sustainable economic growth. In the short term, it may be possible to eliminate the effects of aging population through better use of available human resources. However, in the longer perspective, this will not be enough to counter unfavorable demographic trends. In this context, it will be necessary to increase the share of the economically active population, and this can be partially done through international migration of highly qualified workers. However, our study shows that the level of immigration of highly qualified workers remains modest in most of the EU countries. In this paper, we are analyzing the causes behind the current situation and are also trying to formulate recommendations for migration policy focused on highly skilled labor. At the same time, we are aware that, while international migration contributes to the accumulation of human capital, it cannot by itself solve the structural issues of European labor markets.