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Scalability and privacy are crucial for the RFID-based supply chain systems. But few existing protocols consider the scalability requirement and they have security and privacy issues more or less. In this paper, aiming at the special needs of the supply chain, we propose a Lightweight Scalable Privacy-preserving protocol, LSP, which only needs to XOR and hash operations. By introducing the reverse hash chain, LSP greatly reduces the burden on the database comparing with the existing constant-time protocols. Based on our analysis, the protocol can guarantee confidentiality, untraceability, forward security and reader authentication as well as high efficiency. Meanwhile, LSP can prevent desynchronization attack. We also use the MICAz sensor nodes to simulate our protocol and the result shows it spends less time.