To promote the construction of an efficient Civics classroom in vocational colleges and universities and achieve the goal of cultivating talents with moral character, this paper proposes a Civics classroom teaching system based on new media technology to enhance the efficiency and effectiveness of Civics teaching. By constructing the AHP teaching system, the hierarchical structure model is divided into target layer Z, criterion layer C, and program layer P, thus constructing a pairwise comparison array and calculating the weight vector to provide integrity support for the construction of the Civics classroom system. In structuring the teaching model, a third-order nonlinear expression is used to transform and upgrade the traditional Civics teaching system, which simplifies the teaching model. To verify the feasibility of the Civic Science classroom teaching system based on new media technology, experiments were conducted on its teaching effect. The results show that the average response time of the proposed system is 15.694ms. The resource preference time is above 0.92, which is better than the 49.12ms of the recommendation system based on knowledge mapping. The average value of pre and post-test performance of students in the experimental class is 0.675, and the positive interest in learning is 45.71±6.03. It can be seen that the new media technology has promoted the Civics course to break through the traditional teaching mode and further enhance the efficient development of the Civics classroom.