Abstract: Efficient task scheduling is critical for grid application to achieve high performance. In grid computing, an application is decomposed into a set of dependent tasks. In the grid environment where resources have different capability and resources are interconnected over the world, the dependence among tasks affects the scheduling strategy greatly. The general task scheduling problem includes the problem of assigning the tasks of an application to suitable resource and the problem of ordering task executions on each resource. In this paper a task-resource assignment graph (T-RAG) is used to represent a potential resource assignment plan. And a model of task scheduling based on optimization selection of T-RAG is proposed, which maps the dependent task scheduling problem into a graph optimization problem. As a result of this optimization selection, the optimal graph is obtained and such optimal graph is the optimal scheduling plan which determines the resource assignment plan and the execution order of tasks. Finally, the task scheduling algorithm based on the proposed scheduling model is implemented. Compared with the ILHA algorithm in the simulation environment, the proposed algorithm shows better performance in the situation of a large body of data transported among tasks and significant differences in resources capability and network bandwidth.