Abstract: Based on the high accuracy compact difference scheme and the alternating group explicit (AGE) iterative method which has obvious property of parallelism,an AGE iterative method with the fourth-order compact scheme is established for the steady convection-diffusion equation.Numerical solutions are obtained for the model problem of natural convection in a square cavity with large Rayleigh number of physical interest and small Prandtl numbers attempted.Some results of the present are compared with the referenced paper.