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. When a virtual network arrives, the recent studies focus on designing a solution to minimize the energy cost while maximizing the revenue of the physical network at that time. However, after some time, due to the significant dynamics of the resources of the physical network, the previous solution may become less energy efficient. In this paper, we take a further step and study how to re-optimize the energy cost by leveraging the migration technique. In particular, we first model the pros (e.g., energy saving) and cons (e.g., interruption time and bandwidth waste) of migration. Then we design a heuristic energy aware virtual network migration algorithm called EA-VNM. It answers the following key questions: when performing migration, migrate which virtual nodes to where, and how to perform migration. Extensive simulations show that our algorithm significantly reduces the energy cost by up to 25% over the state-of-the-art algorithm while maintaining similar revenue.