In this paper, we propose a new model for the multi-objective multiple allocation hub network design and routing problem which contains determining the location of hubs, the design of hub network, and the routing of commodities between source-destination pairs in the given network. The selected hubs are not assumed to be fully connected, and each node and arc in the network has capacity constraints. The multiple objectives of the problem are the minimization of total fixed and transportation costs and the minimization of the maximum travel time required for routing. We propose a mathematical formulation for the multi-objective problem and present a meta-heuristic solution based on a well-known multi-objective evolutionary algorithm. Using the proposed formulation, we are able to find the optimal solution for small networks of five nodes and seven nodes. To evaluate the performance of our heuristic approach on real data, the computational experiments are conducted on Turkish postal system data set. The results demonstrate that our heuristic approach can find feasible solutions to the problem in reasonable execution time, which is less than 10 min.