This study utilized the secondary data of recent accreditation results of undergraduate training programs, and in-depth interviews with five peer reviewers to assess the status of and the challenges facing those programs to meet the learning outcomes required by the Vietnamese Quality Framework (VQF). The results reveal that 605 training programs at university undergraduate level were accredited according to the Circular No. 04/2016-TT-BGDĐT that had been promulgated by the Vietnam Ministry of Education and Training. Of these programs, two made up the bulk, namely Business and Management, and Education Science and Teacher Training. In terms of expected learning outcomes, the study showed a large number of the training programs in the fields of business and management, and education science and teacher training failed to meet criteria. The research results also identified limitations and challenges of the training programs relating to meeting the demands of expected learning outcomes regulated in the VQF. In addition, suggestions are made for ways higher education institutions and the authorities can contribute to improving the quality of training programs at higher education institutions.