A new preconditioned matrix was introduced for solving linear systems with Gauss-Seidel iterative method.Under the condition that the coefficient matrix being an M-matrix

which is widely used

the comparison theorem between preconditioned Gauss-Seidel iterative method and classic Gauss-Seidel iterative method was given.The preconditioned Gauss-Seidel iterative method is convergent and it accelerates the convergent speed of classic Gauss-Seidel iterative method.It showed that newly proposed preconditioned Gauss-Seidel iterative method is superior to the Gauss-Seidel iterative method mentioned.A numerical example was given to verify the effectiveness of the conclusions.