Recently, many hash-based authentication protocols were presented to guarantee mutual authentication between tag and DB in RFID system. To be suitable for distributed DB environment, one generally uses fixed constant value as a tag ID. However, some existing protocols have security flaws or heavy computational loads in DB in order to search a tag ID. We propose a secure authentication protocol which is suitable for distributed DB environment by using unchangeable tag ID. The storage method of pre-synchronized information in DB at previous session is core idea of our proposal which gives low-cost ID search of DB at next session. In normal synchronization state, our protocol only requires 3 hash operations in tag and DB respectively.