In the last twenty years, secure group communication has received ever increasing interest. Many rekeying schemes have been proposed in the literature that are both scalable and able to fulfil backward and forward security in a dynamic group model. However, all these schemes assume a single-group model and thus are not efficient when applied to a class of ermerging applications that require a more general multi-group model, where groups may overlap both partially and totally. In this paper, we present MG-LKH, a new centralised rekeying scheme for a dynamic multi-group model that is scalable in terms of storage, computing, and, especially, communication with respect to the number of users and the number and size of groups. Furthermore, we evaluate MG-LKH performance and compare it to traditional rekeying schemes adapted to the multi-group scenario.