The design of a secure authentication scheme for Radio Frequency Identification (RFID) systems has been extensively studied in recent years in view of the awareness of individual privacy and the requirement of robust system security. However, based on security analyses conducted by other researchers and us, most of the proposed authentication schemes suffer a variety of security threats, privacy violation problems and heavy computation workload at the server. In this study, we introduce a mutual authentication scheme for resource-constrained RFID tags. Security analysis of proposed scheme and performance comparison with other schemes are done to show that our scheme can enhance data security, provide privacy protection and improve backend system performance for a generic RFID system with low-cost RFID tags.