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In the paper, an improved two-grid scheme based on shifted-inverse power method is proposed to solve the elliptic eigenvalue problems. With this new scheme, the solution of the elliptic eigenvalue problem on a fine grid T h is reduced to the solution of the elliptic eigenvalue problem and the recovered eigenfunction on a much coarser grid T H , and the solution of an elliptic boundary value problem and the recovered solution on the fine grid T h . Theoretical analysis shows that the scheme allows a much coarser mesh to achieve the superconvergence rate. Finally, some numerical experiments are carried out to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]