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The integration of Civics elements into the EFL classroom is an organic supplement and deepening of the teaching content and materials, while EFL Civics classroom teaching is a powerful means to strengthen the deep and longitudinal development of students’ critical thinking. This paper discusses the relationship between EFL Civics classroom teaching and the development of critical thinking ability from the theoretical and practical levels respectively. On the basis of existing research, the evaluation index of students’ critical thinking ability is proposed. The CVM coefficient of variation method is improved, and the ICVM and BP neural network algorithm are combined to constitute the evaluation model of students’ critical thinking ability based on ICVM and BP neural network. According to the evaluation process, the level of students’ critical thinking ability after EFL-based Civics classroom teaching is derived. It also integrates teachers’ and students’ evaluation of the effect of English Civics elements integrated into the EFL classroom, and finally obtains the practical teaching effect of the EFL Civics classroom. The overall mean value in the teacher’s side is greater than 3.5 points, which indicates that teachers are basically positive about the effect of integrating Civics in EFL courses, and basically agree with the positive impact of English Civics elements on EFL classroom teaching. Based on the evaluation results of ICVM and BP model, the evaluation scores of students’ critical thinking skills and critical thinking monitoring are higher than the evaluation scores of critical thinking tendency, i.e., the elements of English Thinking can be effectively integrated into the EFL classroom and promote the development of students’ critical thinking skills.