In this paper, one kind of Gauss-Seidel type monotone iterative solution and its stability for a class of nonlinear convection reaction-diffusion problems with functional reaction terms and nonlocal boundary conditions are studied by the upper and lower solutions method and monotone iterative technique. Using the monotone iterative method, the maximal and minimal solutions, the existence and uniqueness, consistent convergence and stability analysis of the solutions are presented together. Finally, the effectiveness and applicability of the Gauss-Seidel type monotone iterative algorithm are verified by a simple model.