Due to the abstract concept and strong logic required for college mathematics courses, students have great difficulty in learning college mathematics, and the students' make-up examination rate and repetition rate are high, which leads to the retaken course. Because times and spaces, the traditional teaching method cannot meet students in the learning needs of retaken courses. As an online and offline mixed teaching mode with high compatibility, flipped classrooms can satisfy the student's personalized learning, so that students can learn in a more flexible and active way and participate more. In order to explore the specific practical effect of flipped classroom and improve the teaching quality of retaken public basic course of college mathematics, based on relevant literature and teaching experiences, the paper analyzes the characteristics of students retaking courses, the retaken courses and flipped classroom, discusses and designs a relatively complete and feasible teaching mode and method in the practice teaching of linear algebra course. The results show that this mode effectively improves students' learning effect, and the students' satisfaction is high.