Due to the ever-growing use of active Internet devices, the Internet has achieved good popularity at present. The smart devices could connect to the Internet and communicate together that shape the Internet of Things (IoT). Such smart devices are generating data and are connecting to each other through edge-cloud infrastructure. Authentication of the IoT devices plays a critical role in the success of the integration of IoT, edge, and cloud computing technologies. The complexity and attack resistance of the authentication protocols are still the main challenges. Motivated by this, this paper introduces a lightweight authentication protocol for IoT devices named Light-Edge using a three-layer scheme, including IoT device layer, trust center at the edge layer, and cloud service providers. The results show the superiority of the proposed protocol against other approaches in terms of attack resistance, communication cost, and time cost.