In this paper, we describe a vulnerability against one of the most efficient authentication protocols for low-cost RFID tags proposed by Song. The protocol defines a weak attacker as an intruder which can manipulate the communication between a reader and tag without accessing the internal data of a tag. It has been claimed that the Song protocol is able to resist weak attacks, such as denial of service (DoS) attack; however, we found that a weak attacker is able to desynchronise a tag, which is one kind of DoS attack. Moreover, the database in the Song protocol must use a brute force search to retrieve the tag’s records affecting the operational performance of the server. Finally, we propose an improved protocol which can prevent the security problems in Song protocol and enhance the server’s scalability performance.