The microservice-based smart grid service (SGS) organization and the heterogeneous multi-cores-based computing resource supply are the development direction of edge computing in smart grid with high penetration of renewable energy sources and high market-oriented. However, their application also challenges the service schedule for edge computing apparatus (ECA), the physical carrier of edge computing. In the traditional scheduling strategy of SGS, an SGS usually corresponds to an independent application or component, and the heterogeneous multi-core computing environment is also not considered, making it difficult to cope with the above challenges. In this paper, we propose an SGS scheduling strategy for the ECA. Specifically, we first present an SGS scheduling framework of ECA and give the essential element of meeting SGS scheduling. Then, considering the deadline and importance attributes of the SGS, a microservice scheduling prioritizing module is proposed. On this basis, the inset-based method is used to allocate the microservice task to the heterogeneous multi-cores to utilize computing resources and reduce the service response time efficiently. Furthermore, we design the scheduling unit dividing module to balance the delay requirement between the service with early arrival time and the service with high importance in high concurrency scenarios. An emergency mechanism (EM) is also presented for the timely completion of urgent SGSs. Finally, the effectiveness of the proposed service scheduling strategy is verified in a typical SGS scenario in the smart distribution transformer area.