Hub location-allocation problems are currently a subject of keen interest in the research community. However, when this issue is considered in practice, significant difficulties such as traffic, commodity transportation and telecommunication tend to be overlooked. In this paper, a novel robust mathematical model for a p-hub covering problem, which tackles the intrinsic uncertainty of some parameters, is investigated. The main aim of the mathematical model is to minimize costs involving: 1) the covering cost 2) the sum of the transportation costs 3) the sum of the opening cost of facilities in the hubs 4) the sum of the reopening cost of facilities in hubs 5) the sum of the activating cost facilities in hubs and 6) the sum of the transporters' purchasing cost. To solve this model, use has been made of the new extensions to the robust optimization theory. To evaluate the robustness of the solutions obtained by the novel robust optimization approach, they are compared to those generated by the deterministic mixed-integer linear programming (MILP) model for a number of different test problems. Finally, the conclusions are presented.