An on-line game is growing of very fast through characters of the interactive Computing and internet environment. In addition, an edu-game combing the advantages of the game and the education increase gradually. The paper proposes an edu-game system for providing knowledge through the hierarchical structure. The system differs from existing ones that combine a game and an on-line education. There are three different goals as follows. First, the paper proposes three-level of knowledge hierarchies. The method enables users to understand more easy and systematic and interesting education. Second, the graphic interface of a puzzle type is able to contact more conveniently and it provides beauties and functionalities. Third, Among them, specifically the knowledge hierarchy is not forced to users and the method also can study in detail and users can enjoy systematically e-education by using the general type of a puzzle game.