In this paper, we address a hub-spoke network design problem for air-cargo systems. To build such a network, three kinds of network costs should be considered: fixed costs for establishing a hub, fixed costs for operating air-cargo on each route and variable costs occurring on each route. With these kinds of costs, we develop an optimization model for designing a hub-spoke network in air-cargo systems, including the hop-count constraint being used effectively to deliver freights. We suggest a dual based heuristic algorithm to solve our problem. Computational experiments show that the proposed heuristic is satisfactory in both speed and the quality of the solutions generated.