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With the increase of data-intensive application, the amount of data that the task requires becomes much larger and the task scheduling performance is greatly affected by the data transfer overhead. In grid, establishing trust model is considered to be an important measure of improving the grid security. Therefore, considering the two problems above, this paper improves the Min-Min algorithm and proposes trust model-based Min-Min scheduling algorithm. This algorithm consists of three phases: data file selecting, task scheduling and data scheduling. Two salient features of this algorithm are: 1) in selecting task-required data files, it considers file server's trust degree and data transmission time, it selects the data file with bigger trust value and smaller data transmission time, 2) in data transmission time calculating and transmission path selecting, it adopts the shortest path algorithm-Dijkstra. The experiment results show that although this scheduling algorithm extends the task completion time, the success rate of task execution is apparently raised.