The proofs of inequalities are a kind of important topics in the process of mathematical analysis teaching,by combining the related knowledge on the proofs of inequalities in all chapters and by generalizing the existed methods for the proofs of inequalities,three methods such as function monotonicity method,mean value throrem method andfuncton convexity method are summarized in order to boost and enhance initial learners to understand and master the methods for proofs of the inequalities.