The solutions to the problems of construction with ruler and compasses are various. The construction problems with ruler and compasses in the junior high school mathematics lessons mostly focus on the basic ones now. For those are difficult to solve, there are some methods to reveal to students. In the view of the current situation, this dissertation tries to organize some methods for advanced construction problems with ruler and compasses and provide a learning channel to students who have interests – how to start and find some key points to solve them. In the dissertation, several methods and examples will be revealed and illustrated by the so-called difficult and advanced construction problems.