The p-hub problem is a facility location problem that can be viewed as a type of airline network design problem. Given a finite set of nodes, each node (city) sends and receives some type of traffic (airline passengers) to and from other nodes (cities). The hub (airport) locations must be chosen from among these nodes to act as switching points. In this paper we consider the uncapacitated p-hub median problem with single allocation, where each non-hub node (origin and destination) must be allocated to exactly one of the p-hubs. We provide a reduced size formulation and a competitive recurrent neural model for this problem. The architecture of the proposed neural network consists of two layers (allocation layer and location layer) of np binary neurons, where n is the number of nodes and p is the number of hubs. The effectiveness and efficiency of the proposed recurrent neural network under varying problem sizes are analyzed. Computational experience with another neural networks and heuristics is provided using data given in the literature.