Many artificial networks in the real world have the power-law degree distribution. This feature causes a lot of difficulties in network design, such as robustness, reliability and other performance issues. In this paper, the congestion problem in power-law communication networks is focused. Since nodes with very large degree usually become the bottleneck in this kind of networks when shortest path routing is adopted, a new design of routing is proposed. A hybrid approach, that combines a genetic algorithm and a greedy approach, is designed to find the routing paths of the source-destination pairs. As shown by theoretical and simulation results, the transmission capacity can be improved with the new design which outperforms other existing routing schemes. It should also be emphasized that, though only scale-free network is discussed, the proposed approach is general and useful for other network types.