In a Radio-Frequency IDentification (RFID) system, the interaction data between an RFID tag and the reader is in a wireless communication mode. Due to the inherent openness of the mode, the interaction data can be easily obtained by a third party. For the sake of data security, a lightweight authentication protocol is designed in this study. A lightweight pseudo-random function is selected as the data encryption algorithm, which can reduce the overall calculation amount of the RFID system and ensure the security of the interaction data. Meanwhile, it can operate on an input parameter of any length and give an output of a fixed length. A comprehensive analysis of the protocol from the perspectives of security, calculation amount, and gate circuit shows that the protocol has high security requirements and the overall calculation amount is also less than those of other protocols in comparison.