This paper establishes the index system for evaluating the maturity of university management capability, constructs the two-by-two comparison matrix through hierarchical analysis, and determines the weight coefficients of each index for maturity evaluation. Finally, the maturity evaluation is carried out with different faculties of University H as a case study, and the results of teaching quality management maturity of different faculties are obtained through self-assessment, and then one of the faculties is selected for fuzzy evaluation. Based on the fuzzy evaluation method, the prioritization matrix of the management capacity improvement program of the faculty was derived and the current problems of the faculty were pointed out. The results of the study show that the faculties in the case study show great variability in different dimensions of teaching quality management, and the difference between faculties with high maturity scores and those with low scores can be as high as 1.66, which indicates that a “one-size-fits-all” management approach should not be adopted even within the university. The College of Media and Design, with a total maturity level of 52.36, is at the defined stage, and there is still a lot of work to be done to standardize and institutionalize its management capabilities. At the same time, this study also gives the strategies and paths for colleges and universities to improve their management maturity.
