Edge computing is emergence for improving the performance of cloud-based and internet of things systems. In this paper, a multi-tag authentication algorithm based on edge computing is proposed. The algorithm regards RFID reader and tag as the nodes of edge computing, and uses the tag and reader's computing ability to process and streamline the security authentication information. The authentication server can perform multiple tags' certification and identify false tags in RFID systems. The algorithm reduces the pressure on the authentication server and avoids many signal collisions in wireless channels. The tag has the ability to calculate the equivalent of the node in the proposed edge computing systems, and handle its own ID to be detected by the reader as 1 bit signal, which can prevent too much information interaction between the tag and the reader, therefore, it can protect the privacy of tags.