Grid computing focuses on making use of a very large amount of resources from a large-scale computing environment. It intends to deliver high-performance computing over distributed platforms for computation and data-intensive applications. In this paper, we will present an effective parallel hybrid asynchronous method to solve large sparse linear systems by the use of a Grid Computing platform Grid5000. This hybrid method combines a parallel GMRES(m) (Generalized Minimum RESidual) algorithm with the Least Square method that needs some eigenvalues obtained from a parallel Arnoldi algorithm. All of these algorithms run on the different processors of the platform Grid5000. Grid5000, a 5000 CPUs nation-wide infrastructure for research in Grid computing, is designed to provide a scientific tool for computing. We discuss the performances of this hybrid method deployed on Grid5000, and compare these performances with those on the IBM SP series supercomputers.