Cell-centered finite difference approximations for second-order convection-diffusion equations of divergence type are considered. Approximation of the convection term in such problems by central finite differences leads to schemes of second order, which are stable only for sufficiently small mesh size \(h\). Therefore a number of modified upwind finite difference strategies is proposed, that provide a second order of accuracy and that are unconditionally stable (i.e. not only for small \(h\)). Furthermore they satisfy the discrete maximum principle. The error estimates are performed in the discrete Sobolev spaces associated with the considered boundary value problem.