Protecting air hub nodes against failure, which may exist because of some unforeseen events like severe weather, terrorism threats, etc., is a significant concern of managers in a strategic level, as reactivation of disrupted hubs would be too costly and time consuming. In this paper, we address a mixed integer linear programming model based on disruption scenarios, for reliable capacitated single allocation hub network design (RCSAHND). For each disruption scenario, our model sets potential backup hubs among available nodes. The objective here is to minimize the nominal cost, when no disruption occurs, as well as reducing the disruption risk using the -robustness criterion. p-robustness is one of the robust optimization measures in the literature, trying to bound the cost in disruption scenarios. To show effectiveness of our reliable design, the failure of some hub nodes through number of scenarios are studied on Iranian Aviation Dataset (IAD). Results show that by imposing trivial change in cost for designing the reliable hub network from the beginning, we will have a more reliable hub network which charges us less when a disruption occurs.