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Due to the huge computing resources the grid can provide, researchers have utilized the grid to run very large scale applications over a large number of computing and I/O nodes. However, since the computing nodes in grid are spread geographically over a wide area, communication latency varies significantly between nodes. Thus, running existing parallel applications over the whole grid can result in a worse performance even with larger number of computing nodes. Hence, in the grid environment, usually parallel applications still run on a cluster. It is expected that the emerging lambda network technology can be used for the backbone networks of grids and improve the communication performance between computing nodes. In this paper, we show the potential benefit of the lambda network for the parallel applications in grid environment. Our measurement results reveal that the NAS parallel benchmark over lambda grid can achieve more than 50% higher performance than a single cluster case. In addition, the results show that the parallel programming library such as MPI still needs to be improved with respect to the tolerance on the network delay and the topology awareness.