The design of the hub-and-spoke network has wide applications in the freight transportation system. This design involves the location of a group of hubs as well as the allocation between nonhub nodes and the hubs after the location. On the basis of the traditional single distribution hub-and-spoke network, the congestion flow waiting model (CFWM) and the congestion flow redistribution model (CFRM) are proposed in this paper after considering traffic waiting and traffic diversion, respectively, in the case of hub congestion. The presented models focus on the design of single distribution hub-and-spoke logistics network under traffic congestion. The objective function minimizes the total cost of the road network on the premise of ensuring the normal operation of the logistics network, which effectively balances the contradiction between the economic benefits of traffic scale and the congestion cost. Given the complexity of the problem, the congestion cost function is linearized, and the mutational particle swarm optimization (MPSO) is employed for the solution. Additionally, certain calculation experiments and sensitivity analysis of the congestion optimization model are conducted to verify the effectiveness and applicability of the constructed hub-and-spoke network and the congestion solutions. The results indicate that the optimized logistics network may effectively alleviate congestion, balance the network freight flow, and improve the stability of the hub-and-spoke network.