Private Universities currently play an important role in the higher education system, contributing to the training of highly qualified human resources for the country. However, the training quality at private universities has been evaluated lower than that at the public ones. One of the main reasons is that the quality assurance at private universities has not been taken care of. Especially, the awareness of managers and teaching staffs on training quality assurance relatively affects their ability to ensure the training quality. This study is conducted to raise awareness of the quality of training and ensure the training quality according to AUN-QA standards for managers and lecturers at private universities in Ho Chi Minh City. The author has proposed solutions to be implemented and methods to implement them to raise awareness of training quality and ensure training quality according to AUN-QA standards.