The current teaching quality evaluation mainly adopts single quantitative or qualitative index type, resulting in the evaluation results are not objective and accurate. In order to improve this deficiency, this paper proposes a new TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method based on intuitionistic fuzzy sets (IFSs), which can solve the hybrid multi-attribute decision-making (MADM) problem with certain and fuzzy indexes. Firstly, we use the intuitionistic fuzzy values (IFVs) to represent the results of qualitative index, and respectively calculate the similarity between the quantitative, qualitative indexes and the ideal, inverse ideal solution using different equations. Through weighted integration, the comprehensive similarity between them can be obtained. Then the proximity between each evaluation object and the ideal object is calculated. Finally, the proposed MADM algorithm is applied to an example of teaching quality evaluation. Through the comparison and analysis of the evaluation results, it is proved that the algorithm proposed in this paper is effective in solving the problem of teaching quality evaluation.