Quality assurance in training applied arts plays an important role in building a sustainable and developed arts education system. It helps colleges determine and maintain the necessary criteria for training programs, thereby improving the quality of education and meeting the increasing needs of society and the labor market. This article presents an overview of managing vocational trainning quality and applied arts training quality - quality assuarance direction at colleges based on some current popular training quality management models and reseach works of foreign countries and Vietnam relating to vocational training management models in vocational school to serve as a theoretical basis to survey the reality and propose solutions quality managing on applied arts training with a assuarance direction at colleges to meet the socail and labor market needs. The research results have shown that there are still many shortcomings in the management of training in applied arts in the direction of quality assurance in colleges today that need to be resolved. Proposing solutions to help colleges improve the quality of training in applied arts in the direction of quality assurance.