In this paper we propose a practical and robust multigrid method for convection–diffusion problems based on a new coarsening techniques for unstructured grids. The idea is to use a graph matching technique to define proper coarse subspaces. Such an approach is based on the graph corresponding to the stiffness matrix, and is purely algebraic. We prove that our coarsening technique preserves the M matrix property. We also give several numerical examples illustrating the robustness of the method with respect to the variations in both the diffusion and convection coefficients. Copyright © 2002 John Wiley & Sons, Ltd.