The hub location problem involves a network of origins and destinations over which transportation takes place. There are many studies associated with finding the location of hub nodes and the allocation of demand nodes to these located hub nodes to transfer the only one kind of commodity under one level of service. However, in this study, carrying different commodity types from origin to destination under various levels of services (e.g. price, punctuality, reliability or transit time) is studied. Quality of services experienced by users such as speed, convenience, comfort and security of transportation facilities and services is considered as the level of service. In each system, different kinds of commodities with various levels of services can be transmitted. The appropriate level of service that a commodity can be transmitted through is chosen by customer preferences and the specification of the commodity. So, a mixed integer programming formulation for single allocation hub covering location problem, which is based on the idea of transferring multi commodity flows under multi levels of service is presented. These two are applied concepts, multi-commodity and multi-level of service, which make the model's assumptions closer to the real world problems. In addition, a differential evolution algorithm is designed to find near-optimal solutions. The obtained solutions using differential evolution (DE) algorithm (upper bound), where its parameters are tuned by response surface methodology, are compared with exact solutions and computed lower bounds by linear relaxation technique to prove the efficiency of proposed DE algorithm.