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One of the hottest issues in RFID system is to design low-cost and practical authentication protocol which is necessary. Many researchers have proposed some lightweight authentication protocols which only use lightweight operations to provide some security properties, such as mutual authentication, untraceability etc. In this paper, we analyze the security of an efficient authentication protocol, OHLCAP, and find its weakness. According to its weakness, we proposed a one-way Hash based low-cost authentication protocol with forward security and analyze its efficiency and security. The results indicate our protocol is suitable for low-cost RFID system on storage cost, communication cost, and computation cost of tags. It can not only provide security properties the original has but also provide forward security and prevents against desynchronization attack.