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Recent years have witnessed the rapid development of Grid computing over the Internet, which promises to empower highly desirable resource sharing and cooperation among different organizations. However, there remains a challenging issue facing Grid environments. Malicious or selfish nodes consume precious resources without contribution or even try to destroy the system intentionally. This can severely degrade the system performance and limit the healthy development of Grid systems. To encourage resource sharing and fight against malicious behaviors, we propose an adaptive resource management framework QGrid which integrates trust factor into economic-driven allocation process. Each provider allocates resources according to the bidding price and the trust value of a requester by controlling the corresponding threshold of price and trust value. The incomplete information is a key issue for a provider in determining the two thresholds. We employ a Q-learning technique to resolve the issue, which can adapt to the dynamics of Grid environments. Furthermore, we introduce a simple isolation scheme to secure the Grid system by frustrating malicious participants from joining the system. A QGrid prototype has been successfully implemented in a real Grid test-bed, CROWN. Theoretical analysis and comprehensive experiments have been conducted, which demonstrate the efficacy of QGrid.