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In order to solve the security and privacy problems of low-cost RFID, in which only 250-3k logic gates can be devoted to security-related tasks. Many protocols have recently appeared, but all of them use traditional cryptographic primitives, which is unsuitable for low-cost tags. Some other proposals use non-cryptographic operations such as XOR and CRC, which have disadvantages in at least one aspect. Most importantly, these schemes can not guarantee data synchronism between tag and reader. In this paper, we provide a lightweight mutual authentication protocol based on tag ID number updating for low-cost RFID. This protocol can solve security problems and have better performance than other mutual authentication protocols.