Considering the heterogeneous structure of scale-free networks causing low traffic capacity of network, we propose to improve the network transport efficiency by rewiring a fraction of edges for the network. In this paper, six edge rewiring strategies are discussed and extensive simulations on Barabási–Albert (BA) scale-free networks confirm the effectiveness of these strategies. From another perspective, rewiring edges for scale-free networks directly reuse the removed edges under some edge-removal strategies [Z. Liu, M. B. Hu, R. Jiang, W. X. Wang and Q. S. Wu, Phys. Rev. E76 (2007) 037101; G. Q. Zhang, D. Wang and G. J. Li, Phys. Rev. E76 (2007) 017101], and can significantly enhance the traffic capacity of the network at the expense of increasing a little average path length. After the edge rewiring process, the network structure becomes significantly homogeneous. This work is helpful for network design and network performance optimization.