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The method GMRES is used widely to solve the large sparse linear systems. In this paper, we will present an effective parallel hybrid asynchronous method, which combines the typical parallel method GMRES with the Least Square method that needs some eigenvalues obtained from a parallel Arnoldi process. And we will apply it on a Grid Computing platform Grid5000. Grid computing in general is a special type of parallel computing. It intends to deliver high-performance computing over distributed platforms for computation and data-intensive applications by making use of a very large amount of resources. From the numeric results, we will present this hybrid method has some advantage for some matrices compared to the general method GMRES.