To solve the problems about securities, absence of calculation pertinence, incapability of making the most of the reader’s computation and storage capacity that emerged in Radio Frequency Identification (RFID) authentication protocols, the paper proposes a Hash function based server/serverless adaptive and mutual authentication protocol of RFID based on the analysis of RFID authentication protocol that using a backend server and without using a backend server. The protocol can automatically switches between the RFID authentication protocol with or without a backend server according to the application range of RFID tags. The BAN logic proof, security and efficiency performances analysis and comparison with other similar RIFD protocols presented by the paper show that the protocol can effectively meets the security requirements of RFID authentication protocols.