In a peer to peer grid computing system, volunteers (i.e., resource provides) with heterogeneous properties can freely join and leave in the middle of their computation. Thus, the system should be adaptive to a dynamic changing environment. In particular, scheduling, result certification, and replication mechanisms must be dynamic and adaptive in such a system. In this paper, we propose a new peer to peer grid computing system based on mobile agents. The proposed system constructs volunteer groups according to volunteers’ dynamic properties such as service time, availability, and credibility. For each volunteer groups, different scheduling, result certification, replication mechanisms are used. These mechanisms are implemented as mobile agents and are conducted in a decentralized way.