Most of the existing solutions on task scheduling and resource management in grid computing are based on the traditional client/server model, enforcing a homogenous policy on making decisions and limiting the system flexibility and scalability. In this paper, we propose a peer-to-peer (P2P)-based decentralised approach, which off-loads the intermediate server by letting the peers in the grid to make the scheduling decision among themselves using their own scheduling policies. A generic architecture for metascheduler on peers, called PGS (P2P grid scheduler), and the task scheduling framework based on PGS have been developed. Both push and pull modes are used for distributing the tasks to peers with the support of load balancing and fault tolerance. A prototype of the proposed architecture and mechanism has been developed and simple performance tests have been conducted.