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At present, most Ad Hoc grid task scheduling algorithms ignore the impact of trust mechanism, resulting in the potential dangerous in the real scheduling. In this paper, the trust model is defined, which satisfies the tasks' trust demands, in order to choose the suitable resource node to be executed in the scheduling. Moreover, a task scheduling algorithm extended from Min-Min algorithm (T-Min-Min) is proposed. The proposed algorithm not only satisfies the trust demand of the user but also considers the resource nodes' energy consumption and load balancing. The simulation suggests that it can effectively shorten the task completion time and the number of failed tasks in the Ad Hoc grid.