In this talk, we study an optimal and stable grid-upwind finite volume method for solving linear elliptic equations with Dirichlet or mixed boundary conditions on rectangular or cubic mesh. As suggested in the optimal weighted upwind covolume method, our method also uses the non-standard upwind grids for the control volumes whose vertex positions are automatically computed from the local Peclet's numbers and may vary a lot in different control volumes of the primary mesh. On the other hand, our discretization basically uses the middle point quadrature and thus has second order truncation errors locally. Through various numerical experiments and comparisons in the two and three dimensions, we demonstrate that our method is not only stable but also has optimal convergence rates even for strongly convection-dominated problems.