The effective functioning of a smart university management system significantly improves higher education institutions’ competitiveness. This study aims to assess the implementation of a smart university management system on the example of Kazakh Ablai khan International Relations and World Languages University. The paper considers elements of a smart university system (smart learning technology infrastructure, smart faculty staff, and smart students) from the university managers’ and students’ viewpoints using the stepwise algorithm to raise the university’s competitiveness. During the study, 2700 students were surveyed to assess the implementation and operation of smart systems at the university, and ten experts (the expert team consists of deans and head of departments) were interviewed to identify the weights of each element. The survey results showed that the technology infrastructure for smart learning at the university is at a lower level (50%) than the competence of the teaching staff (60%) and students (89%). Furthermore, based on standardized factor scores and the weighted average, the implementation level of a smart university management system is low – C (0.498), where the weighted assessment of smart learning technology infrastructure is 0.2, smart teaching faculty – 0.19, and smart students – 0.108. According to the results, the university management needs to develop the smart learning technology infrastructure (free Wi-Fi, smart education environment, and smart classrooms) and improve the qualifications of its teaching staff (knowledge and skills, content of the courses, and educational process).