Topology is a majority course for mathematics and applied mathematics majors in normal universities, because the course content is very abstract, teachers find it difficult to teach and students find it difficult to learn, therefore, it is imperative to reform the teaching of topology. Firstly, we have analyzed the problems existing of topology course in the actual teaching process, then, We have carried out beneficial reform and exploration on the teaching design of this course based on years of teaching experience, and have put forward some measures to improve the teaching quality.