In order to cope with the energy crisis, the concept of an energy internet (EI) has been proposed as a novel energy structure with high efficiency which allows full play to the advantages of multi-energy coupling. In order to adapt to the multi-energy coupled energy structure and achieve flexible conversion and interaction of multi-energy, the concept of energy routing centers (ERCs) is proposed. A two-layered structure of an ERC is established. Multi-energy conversion devices and connection ports with monitoring functions are integrated in the physical layer which allows multi-energy flow with high flexibility. As for the EI with several ERCs connected to each other, energy flows among them are managed by an energy routing controller located in the information layer. In order to improve the efficiency and reduce the operating cost and environmental cost of the proposed EI, an optimal multi-energy management-based energy routing design problem is researched. Specifically, the voltages of the ERC ports are managed to regulate the power flow on the connection lines and are restricted on account of security operations. An artificial neural network (ANN)-based reinforcement learning algorithm was proposed to manage the optimal energy routing path. Simulations were done to verify the effectiveness of the proposed method.