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As low-cost RFID tags with limited resource dominate in most of RFID applications, almost all security protocols used between the tag and reader are lightweight protocols which only need to implement some simple operations, such as hash function and XOR operation etc. In this paper, it is analyzed the security of different protocols based on the hash function. Afterwards, we find the A-SRAC protocol has preferable security property but its tag's cost is higher. According to this shortcoming, we propose an improved A-SRAC authentication protocol and analyze its performance and security. The result indicates that this protocol remains all merits of A-SRAC. It does not increase the computational amount obviously and has preferable security with decreased tag's cost.