We investigate the minimum-weight connected subgraph problem. The importance of this problem stems from the fact that it constitutes the back bone of many network design problems having  applications in several areas including telecommunication, energy, and distribution planning. Weshow that thisproblemis NP-hard, and we propose a new polynomial-size non linear mixed-integer programming model.We apply the Reformulation-LinearizationTechnique (RLT) to linearize the proposed model while keeping a polynomial number of variables and constraints.