A smart grid (SG) is an advanced power grid system deployed in a cloud center and smart meters (at the consumer end) that provides higher reliability, better data protection, improved power efficiency, automatic monitoring, and effective management of power consumption. However, an SG also poses certain challenges that need to be addressed. For example, data provided by a smart meter are time sensitive and cannot handle high latency in an SG. Moreover, a smart meter depends on the memory, energy, and other factors. In addition, the security between a cloud center and smart meter is an important issue that needs to be resolved. Edge computing, which is an extension of cloud computing deployed in an edge network between a cloud center and the end devices, is an efficient solution to the above-mentioned issues. Therefore, in this study, we propose a secure mutual authentication protocol based on edge computing for use in an SG.