Abstract: To improve iteration efficiency of high-order discontinuous Galerkin finite element (DG) method, an efficient implicit generalized minimal residual (GMRES) method has been applied to DG method based on unstructured grids. The method is implemented by the ksp solver of portable, extensible toolkit for scientific computation (PETSc) library. In order to further improve computational efficiency of GMRES, the exact calculation method of Jacobian matrix is developed. The Jacobian matrix of Roe scheme and bassi rebay 2 (BR2) scheme are exactly obtained for the freedom of conservation variables. The developed method is applied to compute a variety of steady inviscid and viscous flow problems. First, a NACA0012 airfoil is used to study the effect of restarted iteration and convergence parameters on the GMRES convergence. The computational efficiencies of the GMRES based on different calculation methods of Jacobian matrix are compared by the inviscid and viscous examples. The computational efficiencies are also compared for the GMRES and LU-SGS iterative method. The results show that the exact calculation method of Jacobian matrix can greatly increase the CFL number of the GMRES for different DG methods. Compared with other methods, the GMRES based on the exact calculation method of Jacobian matrix has higher computational efficiency, and its convergence speed is improved by more than one order of magnitude.