The rapid growth of the Internet raises the importance of resource planning of Internet protocol (IP) over elastic optical networks (EONs), which is a challenging task due to more complex and obscure physical -constraints of it. Compared with network cost, the power consumption may eventually become the barrier to the expansion of the Internet. We present an energy-efficient virtual topology design (VTD) scheme for IP over EON. We explicitly explain and analyze the mixed integer linear programming model and the heuristic algorithm for this scheme. Numerical results show that the proposed VTD scheme can significantly save power consumption.