Knowledge base system (KBS) is an organization to store and manage a lot of knowledge. Extension knowledge representation (EKR) based on extension theory is presented in this paper. Two key concepts of EKR are the described——formal semantic of EKR and the formal representation of contradictory problem solving. The basic element of the former is knowledge matter-element model. In addition, the Specific Extension Inference (SEI) corresponding to EKR is also reviewed. The feature of SEI is correlative inference, which has been implemented by computer. Finally, the feature and the frame of extension knowledge base system (EKBS) are proposed. EKBS uses EKR and is an excess of traditional KBS. It is composed of goal system, condition system, common knowledge base, categorized knowledge base, inference machine and knowledge base management system.