It is presented a robust multilevel algorithm for convection-diffusion and anisotropic differential equations. The multilevel algorithm consists of semi-coarsening and line relaxation. It is proved that the convergence of the W-cycle is less than 0.2 independent of the size of the convection term in one direction and the meshsize. The convection term may have turning points. The multilevel algorithm can also be applied to anisotropic elliptic equations with singularities in the coefficients.