In network virtualization, one of the key problems is to embed a sequence of virtual networks with both node and link constraints onto the physical network, which is known to be NP-hard. Recent studies focus on how to minimize the energy cost while maximizing the revenue of the physical network when the VN request arrives. However, after a period of time, due to the dramatic dynamics of the resources of the physical network, the previous solution may become less energy efficient. In this paper, we study how to re-optimize the energy cost by leveraging the migration technique. In particular, we first give the problem model of virtual network migration. Then we design two energy aware virtual network migration algorithms called EA-VNM and EA-VNM-G. For EA-VNM, it answers the following key questions: when to perform migration, migrate which virtual nodes to where, and how to perform migration. Especially, for EA-VNM-G, it further reduces the high time complexity problem of EA-VNM by grouping the virtual nodes to be migrated with fewer conflicts. Extensive simulations show that EA-VNM significantly reduces the energy cost by up to 25% over the state-of-the-art algorithm while maintaining similar revenue and EA-VNM-G reduces the running time significantly.