Aiming at the problem of channel insecurity caused by wireless transmission in mobile Radio Frequency IDentification (RFID) system, a low-cost mobile mutual authentication protocol based on the Hash function was proposed by considering the complexity of the protocol and the implementation cost of the tag. In the protocol, the square operation was used to dynamically update the tag identifier. And the reader identifier, the pseudo random function and Hash function were used to enhance the identity authentication between the reader and the back-end server, which can improve the mobility of the system. Compared with the typical authentication protocols based on the Hash function and the tag ownership transfer protocol, this proposed protocol can resist tracking, impersonation, replay, man-in-the-middle, Denial of Service (DoS) attacks, etc., which can ensure the security of tag ownership transfer. The efficiency of calculation and storage was analyzed, and the results show that the calculation of the tag is reduced and the storage capacity is lower.