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In this paper, we obtain the first error estimate in L2-norm for the classical two-grid method, then design an improved two-grid method by adding one more correction on the coarse space to the classical two-gird method. Furthermore, we also present the error estimates in both L2-norm and H1-norm for the improved two-grid method. Especially, the L2 error estimate of the improved two-grid method is one order higher than that of the classical two-grid. At last, we confirm and illustrate the theoretical result by some numerical experiments.