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 L2error 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.