In wireless sensor network (WSN), the energy of sensor nodes is limited. Designing efficient routing method for reducing energy consumption and extending the WSN's lifetime is important. This paper proposes a novel energy-efficient, static scenario-oriented routing method of WSN based on edge computing named the NEER, in which WSN is divided into several areas according to the coverage of gateway (or base station), and each of the areas is regarded as an edge area network (EAN). Each edge area network is abstracted into a weighted undirected graph model combined with the residual energy of the sensor nodes. The base station (or a gateway) calculates the optimal energy consumption path for all sensor nodes within its coverage, and the nodes then perform data transmission through their suggested optimal paths. The proposed method is verified by the simulations, and the results show that the proposed method may consume about 37% less energy compared with the conventional WSN routing protocol and can also effectively extend the lifetime of WSN.