Abstract: The dynamic and heterogeneous nature of grid resources is a great challenge to static scheduling strategies of dependent tasks. A new static scheduling model based on RT-RAG (reduced task-resource assignment graph) and algorithm are proposed which are more suitable for the grid heterogeneity and support unified scheduling/rescheduling process. The (re) scheduling problem based on the model is thus regarded as an optimization selection problem of RT-RAGs. The experimentation shows that the static scheduling algorithm has better adaptability to grid dynamic and heterogeneity and keeps greatly its superiority up in comparison to the dynamic one and it is also better than the AHEFT algorithm based on the DAG task graph model, especially in case of great resources heterogeneity.