Network virtualization is a promising approach for resource management that allows customized Virtual Networks (VNs) to be multiplexed on a shared physical infrastructure. A key function that network virtualization can provide is Virtual Network Embedding (VNE), which maps virtual networks requested by users to a shared substrate network maintained by an Internet service provider. Existing research has worked on this, but has primarily focused on maximizing the revenue of the Internet service provider. In this paper, we consider energy-aware virtual network embedding, which aims at minimizing the energy consumption for embedding virtual networks in a substrate network. In our optimization model, we consider energy consumption of both links and nodes. We propose an efficient heuristic to assign virtual nodes to appropriate substrate nodes based on priority, where existing activated nodes have higher priority for hosting newly arrived virtual nodes. In addition, our proposed algorithm can take advantage of activated links for embedding virtual links so as to minimize total energy consumption. The simulation results show that, for all the cases considered, our algorithm can improve upon previous work by an average of 12.6% on acceptance rate, while the consumed energy can be reduced by 12.34% on average.