Abstract: Three basic structures have been proposed to organize the task queues for shared-memory multiprocessor systems: centralized, distributed, and hierarchical structures. The hierarchical structure intends to combine the advantage of the other two structures and eliminate their disadvantages. Unfortunately, we find it still has serious load imbalancing, in particular when the workload is heavy and irregular. We propose the use of a forest structure in place of a hierarchical one. Simulation shows the proposed structure can provide better load balancing and less contention than the hierarchical one.