We describe a peer-to-peer self-organizing overlay network for our global computing system. The preliminary simulation results show that the network has some small-world characteristics such as higher clustering coefficient and short path length, which leads to an efficient heuristic task scheduling algorithm on which any volunteer peer with limited knowledge about the global network can dispatch its excrescent computation tasks to powerful nodes globally, in a way contrary to the current global computing system in which a global broker is responsible for the task scheduling. We argue that our approach is a starting point to eliminate the broker component which makes current global systems unscalable.