The conventional computing Grid has developed a service oriented computing architecture with a superlocal resource management and scheduling strategy. This architecture is limited in modeling computer systems with highly dynamic and autonomous computing resources due to its server-based computing model. The super-local resource management and scheduling strategy also limits the utilization of the computing resources. In this paper, we propose a multi-agent based Peer-to-Peer Grid computing architecture. This novel architecture solves the above issues, while provides reasonable compatibility and interoperability with the conventional Grid systems and clients. The main characteristics of this architecture are highlighted by its promising performance and scalability, and its adaptive resource management and scheduling mechanisms. With this architecture, it is promising to build large scale high performance commodity computing Grids at low cost.