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Resource allocations determine an important management task for operational Grids and networks, especially under the constraint of commercially offered resources. Therefore, the need for an optimal allocation of this task arises, and this paper proposes a trust-incentive-based combinatorial double auction algorithm for these resource allocations in Grids. The key and new contribution is the design of a trust-incentive mechanism, which is integrated into an existing combinatorial double auction algorithm (a) to improve the performance of Grid resource allocation and (b) ensure that trust values of participating bidders (typically Grid users, termed peers) are considered. In the newly developed trust-incentive-based algorithm, each peers' trust value is adopted to adjust their bids in the process of the combinatorial double auction. After each transaction, peers participating in the transaction rate each other to setup and update the bilateral trust relationship. Those simulation results obtained demonstrate that the algorithm proposed can improve the efficiency of resource sharing greatly by providing applicable incentives to trustworthy peers to contribute more resources. Moreover, this algorithm can identify and eliminate malicious peers in the system to enhance the Grid security level in that respect.