This paper constructs the ADDIE-F teaching model based on the ADDIE model by introducing the feedback link and carries out the design of Civics teaching methods in colleges and universities based on the model. For the teaching of Civics in colleges and universities, the research object and the selection of teaching experimental methods are designed, and the index system is constructed to evaluate the quality of Civics teaching. The entropy weight method was utilized for the calculation of indicator weights, and the TOPSIS method was used for evaluating the quality of Civics teaching. In order to verify the timeliness of the method given in this paper for promoting the comprehensive development of students as well as student management, this paper carries out a practical application analysis. The results illustrate that the average score of the experimental class before and after the Civics teaching design experiment is 78.52, which is 15.06 points higher than that before the experiment, and the students’ comprehensive literacy situation shows a significant difference at the 5% level. Thus, the Civics teaching design based on the ADDIE-F teaching model under the guidance of comprehensive development can promote the improvement of students’ Civics literacy.