Computational Grids provide computing power by sharing resources across administrative domains. This sharing, coupled with the need to execute distrusted task from arbitrary users, introduces security hazards. This study mainly examines the integration of the notion of “trust” into resource management based on Grid economic model to enhance Grid security. Our contributions are two-fold: First, we propose a trust function which based on dynamic trust changing and construct a Grid trust model based on behavior. Second, we present trust-aware time optimization scheduling algorithm within budget constraints and trust-aware cost optimization scheduling algorithm within deadline constraints. The performance of these algorithms excels that of algorithm without considering trust via theory analysis and simulation experiment.