Resource discovery is one of the important research issues in grid computing. As computational resources are fundamental resources supporting various grid applications, it is of great importance to study computational resource organization and discovery. However, existing approaches are limited in terms of efficiency, scalability, adaptability and the ability to support a wide range of query mechanisms. After analyzing the requirement of application resources, this paper introduces the primary attribute (PA), and describes a computational resource. Then it proposes resource category tree (RCT) to organize and discover the computational resources. This paper presents the mechanism of organizing resources based on RCT, including the basic concepts and rationale, the self-organizing design to support resource dynamics, the load-aware self adaptation and primary-backup based fault tolerance. It also designs four searching algorithms to support comprehensive query types in the framework of resource organization by using RCT, and a theoretical complexity analysis is presented as well. In the end, the paper evaluates the performance of RCT through simulations.