The transport efficiency of a network strongly depends on the underlying structure. The traffic capacity of one real network may be actually very small due to the heterogeneous degree distribution of the network under the global shortest path routing strategy. For the purpose of improving the traffic capacity of the network, in this paper, we propose three edge rewiring strategies. Extensive simulations under the efficient routing (ER) and the shortest path (SP) routing are applied to verify the effectiveness of the proposed edge rewiring mechanisms. It is found that the traffic capacity of the network can be substantially enhanced and the edge rewiring strategies are beneficial to the improvement of overall traffic handling and delivering ability of the network, especially under the SP routing strategy. The edge rewiring methods can be used incrementally to ameliorate the network transportation performance by network service providers.