Exploring the evaluation of the teaching quality of colleges and universities for applied talent cultivation in the context of big data is to be able better to improve the teaching level of colleges and universities. In this paper, the multi-indicator evaluation method is explained, and the commonly used teaching quality evaluation methods, i.e. hierarchical analysis, entropy weight method and gray correlation analysis, are cited. The basic principle of the hierarchical analysis method is given, the initial weight calculation steps of AHP method are illustrated, and the initial weights of AHP method are combined and solved using the entropy weight method. The evaluation principle of the gray correlation analysis method is given, and the combined weights of the AHP-EWM evaluation are illustrated using the gray correlation analysis method. Finally, universities’ teaching quality evaluation indexes for applied talent cultivation were constructed using the AHPEWM evaluation method, and the indexes were mined and analyzed respectively. From the indicators of theoretical literacy and professional research ability, the overall evaluation of the teaching quality of colleges and universities is 92.77% above the C grade. From the indicators of innovation practice and moral quality, the percentages of students’ evaluation of teaching quality in colleges and universities with A, B, C and D grades are 49.02%, 28.6%, 5.12% and 7.25%, respectively. This shows that the evaluation of teaching quality in colleges and universities is multifaceted, and colleges and universities can improve their teaching level according to different evaluation factors.