A discrete gradient for piecewise constant functions is constructed. This discrete gradient exhibits several advantages: it is easy and cheap to compute, and it provides a simple scheme for the approximation of anisotropic convection-diffusion problems. Main result: The authors show a weak convergence property of the discrete gradient to the limit of the sequence of functions, together with a consistency property, both leading to the strong convergence of the discrete solution and of its discrete gradient in the case of a Dirichlet problem with full matrix diffusion. The precise proof that the discrete gradient to satisfy a strong convergence property for the interpolation of regular functions, and a weak one for functions bounded in an \(H^1\) norm is proposed. Numerical tests show the actual accuracy of authors’ method.