Counterfeiting is one of the most serious problems in the consumer market. One promising approach for anti-counterfeiting is to attach a low-cost Radio-frequency Identification (RFID) tag to the product authentication. In this paper, we propose an RFID system for detecting counterfeiting products. This RFID system consists of the tag authentication protocol and the database correction protocol. We use the tag authentication protocol for authenticating tags without revealing their sensitive information. This protocol also allows the customer to freely inquire the tag. To prevent the widespread of the counterfeit products, we use the tag status information along with tag identity information. Meanwhile, the database correction protocol guarantees the correctness of the tag status. Our anti-counterfeiting system is the first work considering the seller who plays an important role in the consumer product supply chain. Finally, we show that anti-counterfeiting system is quite secure against counterfeiting and the tag authentication protocol is lightweight enough to be implemented in RFID-based applications.