With the building of the energy Internet of Things (IoT), the establishment of a private network dedicated to the control and management of the grid to provide reliable and secure power services is attracting more and more attention. Meanwhile, owing to the rapid development of wireless wideband communication technologies, today's wireless communications are increasingly considered by power communication services as a means to serve as the supplementary method to fiber-optics to extend the smart grid services to places where the traditional wired communication technology cannot reach. Based on services demand analysis, this paper proposes a dual-band-dual-network architecture to satisfy the demands in power wireless private network (PWPN). Firstly, we introduce the structure of the PWPN in energy IoT. Then we analyze the requirements of the energy IoT on the PWPN. Finally, we propose a dual-band-dual-network architecture to fulfill most of the PWPN requirements.