As an important basic course in colleges and universities, college mathematics public course plays a very important role in cultivating students' abstract thinking ability, logical reasoning ability and spatial imagination, and lays a good foundation for students to learn other courses. 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. Therefore, it is a difficult problem in colleges and universities to do a good job in the teaching organization and implementation of retaken courses, improve the teaching effect and help students complete their studies. 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. The implementation of flipped classroom teaching mode can better meet students' learning needs in retaken courses. In order to explore the specific practical effect of flipped classroom and improve the teaching quality of retaken college mathematics public basic course, based on relevant literature and teachers' own 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 model and method. Taking linear algebra as an example, these models and methods are put into practice. The results show that this model effectively improves students' learning effect, and the students' satisfaction is high. Through these teaching design and practice, it is expected to inspire relevant teachers' teaching and students' learning, and provide reference for the education and teaching reform of relevant courses in colleges and universities.