In this study, we propose an new approach for solving a quadratic programming problem with diagonally dominant M-matrix and box constraints. This approach is based on the preprocessing technique, as well as an algorithm inspired by a method of Voglis and Lagaris. The principle of this approach is to apply a preprocessing technique initially to reduce the size of the original problem. The preprocessing step allows to identify certain active and inactive indices at the optimum, in order to fix in advance the corresponding values of certain variables, and put the others in the support set \(J_S\) . In order to solve the resulting reduced problem, we then developed an approach inspired on the method of Voglis and Lagaris which falls into the category of exterior point and active set techniques (Kunish and Rendl). Using the notion of support for an objective function developed by Gabasov et al., our approach leads to a more general condition which allows to have an initial pseudo-solution, related to a coordinator support and close to the optimal solution.