The infrastructures such as the internet networks, and phone networks, and their traffic capacity are well discussed in the field of network science. However, there is another type of communication infrastructure, such as the wireless sensor networks, which are usually deployed in tough environments to perform specific tasks. This kind of network usually has limited power supply, and thus the main issue is how to make good use of the energy and prolong the network lifetime. In this paper, we investigate the transport process in power-limited communication networks. We use the complex network models to generate the scale-free networks. We assign each node E0 (a constant) unit of energy and an infinite queue with the first-in-first-out rule for buffering packets. In the traffic model, every node generates packets with a constant rate . The packets' destination nodes are randomly chosen from the network. At each time step, every node delivers at most C packets. If a packet's destination node is among the neighbors of the current node, the packet will be delivered to the destination node directly and then be discarded from the destination node. Otherwise, the packet will be forwarded to a neighbor of the current node with a given routing strategy. In the delivery of a packet, the node consumes a fixed amount of energy, and will die out when it uses up its energy. We propose a hybrid routing strategy for the power-limited scale-free networks based on both the node energy and the shortest path. Specifically, in the routing strategy, we consider the residual energy of neighbor nodes and the shortest path lengths between the neighbor nodes and the destination, and utilize a free parameter to adjust their relative importance. Simulation results demonstrate that there are optimal control parameters which correspond to the maximum network lifetime and the maximum number of delivered packets. According to the proposed routing strategy, we further study the relation between the network topological structure and network lifetime. We find that the more homogeneous the network, the larger the maximum network lifetime is. Moreover, we obtain that the maximum network lifetime gradually increases with the average node degree increasing, but almost decreases linearly with the network scale increasing. In this paper we discuss the network lifetime from the perspective of network science, and give more insights into the transport process on complex networks. In addition, our work provides some clues of how to design the efficient routing strategies for the power-limited communication networks.