With the integration and development of smart grid and 5G communication technology, more and more intelligent terminals are applied to the smart grid system. Aiming at the problem of diversion processing of massive power services, a service scheduling and resource allocation scheme considering the priority of power service is proposed. Firstly, the edge computing processing architecture based on software defined network for smart grid is introduced, and the service processing models are established. Secondly, the service scheduling mechanism based on preemptive priority queuing is elaborated, the mathematical models of service offloading revenue and offloading cost are established with overall system revenue maximization as the objective function. Based on the offloading effectiveness of power service, the resource allocation threshold of each priority service in the mobile edge computing (MEC) server is obtained and taken as the constraint condition. Thirdly, the improved genetic algorithm (IGA) is used to solve the optimal offloading and resource allocation decisions. Finally, the simulation results demonstrate that IGA outperforms other comparative algorithms in terms of convergence speed and individual selection, and the proposed scheme reduced the average processing time, energy consumption, and average processing time of high priority services by 69.2%, 67.7%, and 73% compared to other methods, respectively. The system revenue is improved by 119% compared to other methods.