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As Grid technologies evolve quickly on Internet, research related to resource scheduling faces new opportunities and challenges. These new technologies, ideas and approaches provide a new environment for researching and developing the economy-based resource scheduling system. Aiming at the hierarchical Grid model, following utility optimization thinking, while an universal flexible utility function is provided for addressing the Grid users' QoS requirements of deadline and budget, this paper proposes a new Grid resource scheduling algorithm, which can not only increase the utilization of resources and system throughput, but also realize cost-time optimization between resource providers and users within Grid systems. On the basis of having described the different functional parts of the proposed algorithm, two kinds of simulative experiments about completion time and cost of tasks are conducted. Finally, the experiment results show that the proposed algorithm is effective.