Abstract: For the linear equations Ax=b, two new preconditioning matrices I+S¯ and I+Sˆ were introduced, and corresponding Gauss-Seidel methods were obtained. It was proved that if the coefficient matrix A of the original system was an H-matrix, then the coefficient matrices (I+S¯)A and (I+Sˆ) A of the preconditioning system were also an H-matrix. The convergence theorems of the new methods were proposed. Finally, numerical example was carried out and the results indicated that the convergence rates of the new preconditioning methods are better than those of the corresponding classical Gauss-Seidel method and the modified Gauss-Seidel method proposed by J. P. Milaszewicz.