Although desktop Grid computing has been regarded as a cost-efficient computing paradigm, the system has suffered from scalability issues caused by its centralized structure. In addition, resource volatility generates system instability and performance deterioration. However, regarding the provision of a reliable and stable execution environment, resource management becomes more intricate when the system is constructed in a fully decentralized fashion without a central server. Scaling the system numerically and geographically is necessary for autonomous network organization, facile adaptation to execution failure and dynamic self-management of volatile resources. In order to develop a fully decentralized desktop Grid computing system securely, we propose an autonomous desktop Grid computing system, Self-Gridron based on a neural overlay network. Self- Gridron supports reliable, autonomous, and cost-effective scheduling which includes eligible resource classification and job management (i.e. allocation, replication, and reassignment). Furthermore, Self-Gridron provides sovereign learning with error correction) and evolves adaptively by itself to system changes or failure on the fly while improving performance.