A peer-to-peer grid computing is complicated by heterogeneous capabilities, failures, volatility, and lack of trust because it is based on desktop computers at the edge of the Internet. In order to improve the reliability of computation and gain better performance, a replication mechanism must adapt to these distinct features. In other words, it is required to classify volunteers into groups that have similar properties and then dynamically apply different replication algorithms to each group. However, existing mechanisms do not provide such a replication mechanism on a per group basis. As a result, they cause a high overhead and poor performance. To solve the problems, we propose a new group-based computational replication mechanism to adapt to a unstable, untrusted, dynamic peer-to-peer grid computing environment. Our mechanism can reduce the number of redundancy and therefore complete many tasks by adaptively replicating computations on the basis of the properties of volunteer group such as availability, credibility, and volunteering service time.