The development of education and science is a priority for Russian state policy. Global trends define the main goals of the Russian higher school modernization. However, these also identify the need to overcome a number of contradictions in Russia’s national higher-education system. Pedagogical, or teacher-training, education is of special importance in the development of the entire educational system in the country. Quality education at all steps – preschool, primary, secondary (general and professional) and higher – depends mainly on the quality of pedagogical education. The modern market of educational services recognizes high quality of education and competences of students as the only advantage point for an academic institution over its competitors. Quality is the only universal commodity in the world market that increases the value of all other goods and services. The authors refer to the category of quality management in relation to higher pedagogical education, and describe the key principles of the system of quality assurance applied at Southern Federal University.