With the arrival of the Internet era, online teaching has gradually become common, and online teaching quality evaluation in the context of big data is of vital significance to the quality of talent cultivation in colleges and universities, and at the same time, assisting offline teaching with online courses is a teaching tool to effectively improve teaching quality. As an extended form of hesitant fuzzy set, normal wiggly hesitant fuzzy set can not only fully retain the initial hesitant fuzzy information of the decision maker (DM), but also deeply excavate the potential uncertainty information behind the initial information, which has strong application and practical value. This paper combines the features of normal wiggly hesitant fuzzy sets (NWHFSs) and the characteristics of online teaching quality evaluation system of colleges and universities under the background of big data, and makes full use of the objectivity of the CCSD weight determination method and the advantage of the robustness of the MULTIMOORA multi-attribute decision-making method, and propose the NWHFSs-CCSD-MULTIMOORA multi-attribute decision-making method under the background of big data. In the example analysis of online teaching quality system evaluation in universities, the effectiveness and superiority of the proposed method in this paper are verified through comparative analysis, and corresponding suggestions are put forward to help universities effectively improve online teaching quality.