The Low duty cycle wireless sensor networks (called LDC-WSNs) can be deployed in harsh environments that humans are difficult to access to perform long-term monitoring and target tracking tasks, and they have broad application prospects. LDC-WSN reduces the energy consumption caused by idle listening, but its end-to-end delay is great. The existing LDC-WSN routing protocols focuses on the reduction of end-to-end delay, but they do not fully consider the balancing of energy consumption of nodes in the network. Therefore, some nodes would consume their energy quickly and die soon. To solve this problem, this paper considers the link quality and node's energy levels, and then propose a novel routing algorithm EADR (energy-aware dynamic routing). In EADR, each node maintains a forward set, which contains a set of neighbor nodes with high quality links. During the data transmission, a sender node would send its data to its neighbors with high decision-making factors, where the decision-making factors are dynamically determined by node's work/sleep schedules and energy levels. Simulation results show that EADR can reduce the end-to-end delay, achieve higher successful rate of data transmission, and extend the network lifetime.