Advance Mathematics is an important compulsory course in higher education.  By virtue of many years of teaching experience in this course, we firstly analyze the importance of Advance Mathematics and the disadvantages of the current teaching model, and then propose that the "problem-driven" teaching mode should be introduced into the teaching process of Advance Mathematics. Moreover, we put forward three examples on how to design a case to make the Problem-Driven teaching mode work well in Advance Mathematics.