The paper summarizes the results of research conducted by domestic and foreign scientists on the existing models of education quality system, the practices of the quality management functioning and approaches to evaluating the indicators of an educational scientific organization activity. The principles of the model of the European Foundation for Quality Management (EFQM) and the model of the balanced scorecard (BSC) are distinguished and analyzed based on the analysis of the practice of the quality management system and its indicators in the course of certifcation and accreditation procedures. The basic criteria and principles of improving the system of university education quality management as an important tool of the university's competitiveness have been determined. The specifc features of the organizational structure of higher education institutions, their functions as a system of socio-economic activity are highlighted; the principles of running the quality management system in higher education institutions are defned. The role and basic elements of the educational activity quality system in the strategic management of higher education institutions are defned. The study proposes a model of sustainable evaluation of the effectiveness of education quality management efciency involving two evaluation components, namely management and evaluation perspectives. Opportunities objects (goals, strategies, partnership, resources, organizational culture, interested parties involvement) and the results indicators (students, customers, employees and other stakeholders satisfaction) were formed. The algorithm for improving the system of ensuring the quality of university educational activities is determined and the need to adapt its practical application to the specifcs of the institution, in particular the management system, education quality and strategic management, is substantiated. It was concluded that the improvement process should be based on the standards and recommendations on higher education quality assurance in the European area, the current national system of education quality assurance and regulatory documents regarding the activities of the system of education quality assurance in a specifc institution. Considering the proposed sustainable system for the management system effectiveness evaluation, the author emphasized that the development of indicators of higher educational institutions activity is to be based on the analysis of the university strategic indicators map. The map is advisable to flexibly adapt the structure of the organization according to the following directions: development, processes, consumers, fnances. For this purpose, it is expedient to choose interconnected strategic prospects for higher education institutions development of and to develop a corresponding system of indicators. It is proved that consistent operation of the university quality management system requires ensuring a connection between the evaluated indicators of all types of higher educational institutions activities and the process of forming university strategic management tasks in the course of working out a development strategy and in achieving the objectives set. Key words: higher education institution, competitiveness, quality culture, educational activity, indicators of the organization's activity, quality assurance system, stakeholders, education quality management.