Each country in the world has its own individual approaches to the quality assurance system of higher education, so the quality of educational services in each country is different. The developing countries should be guided by the standards and recommendations put forward by the world's leading countries in the field of the assurance system of higher education in order to improve the quality of education services. The purpose of the scientific investigation is to formulate the objectives and analyze the practical aspects of functioning of the quality assurance system of higher education. In the study's framework of the practical aspects of the higher education's quality in European Union's countries, the methods of general analysis have been used, including comparison and grouping; at the same time, the presentation of statistics is also demonstrated by graphical methods. The practical aspects of quality assurance of higher education in European Union's countries have been analyzed, which is reflected in the dynamics of the number of students who have received higher education, the structure of higher education degree seeking applicants, the employment rate of graduates who have graduated from higher education institutions (Employment rates of recent graduates), the World University Rankings, the Europe Teaching Rankings, rating of the strength of the higher education system (the QS Higher Education System Strength Rankings). Proposals for ensuring the proper quality of higher education and a high level of educational services to educational institutions of the European Union have been presented.