This study addresses the problem of predicting student performance by proposing a heterogeneous transfer learning method based on FMBCC-FT, which aims to accurately predict students’ Civics knowledge mastery. The study achieves effective knowledge transfer by defining university Civics teaching as the source domain and considering the university’s demand for students’ Civics dynamics as the target domain. After collecting and standardizing students’ Civics education data, this study constructed a knowledge base model of Civics teaching based on the source domain data and migrated it to the target domain. To compensate for the bias in the migration, the study designed a three-stage iterative optimization migration weight learning method, which significantly improved the quality of Civics teaching by updating the parameter weights of the source domain model. The process was verified through the experimental control group pre and post-tests. The results showed that the total score of critical thinking ability pre and post-tests was −3.39. The students’ innovative consciousness score in the experimental group was 3.96, which was significantly higher than that of the control group, which was 0.18. In addition, the scores of the quality dimensions of the students in the control group and the experimental group ranged from 3.22 to 3.40 and 3.43 to 3.68, respectively. This empirical result effectively confirms that the Civics teaching model proposed in this paper can effectively improve students’ critical thinking ability, innovation consciousness and overall quality, which is of great guiding significance to the current practice of Civics teaching in colleges and universities.