It's difficult to describe 2 _D objects and more complicated ones with string grammar, for it can't be used to define the complex relations among them. This paper presents the concept of relation graph and its properties. As a new type of grammar, relation graph grammar is able to abstract the attributes of complicated objects conveniently and provide tools to analyze and recognize them. Relation graph grammar can be used in many fields such as pattern recognition, high dimensional text analysis and visual languages. To make the grammar applicable, the recognition and the matching algorithms of it are also introduced respectively.