With the rapid development of China''s economy，the rising residential electricity demand and the increasing varieties of electrical equipment have made the reliability and stability of the new smart grid equipment widely concerned. However，relying solely on the traditional single network architecture often fails to answer the data requests of large-scale grid equipment. To this end，this paper first proposes a cost optimizing model under ultra-dense edge computing networks in regard to the request from the smart grid user side；secondly，considering the influence of the price of communication resources and computing resources on the offloading strategy， the resource utilization cost is taken as an optimizing objective； finally，in order to improve the service quality requested by power grid equipment，considering the task offloading strategy of energy consumption and delay constraints，a Lévy flight-Mayfly Particle Swarm Optimization （Lévy-MAPSO） algorithm is proposed. The experimental results show that different prices have a significant impact on the resource utilization cost. Compared with PSO and Lévy-MA algorithms，Lévy-MAPSO algorithm has the lowest resource utilization cost and the best performance thanks to its population diversity and powerful searching ability.