Radio Frequency IDentification (RFID) technology has been increasingly integrated into numerous applications for authentication of objects or individuals. However, because of its limited computation power, RFID technology may cause several security and privacy issues such as tracking the owner of the tag, cloning of the tags and etc. Recently, two chaotic map-based authentication protocols have been proposed for low-cost RFID tags in order to eliminate these issues. In this paper, we give the security analysis of these protocols and uncover their weaknesses. We prove that these protocols are vulnerable to tag tracing, tag impersonation and de-synchronization attacks. The attack complexity of an adversary is polynomial and the success probability of these attacks are substantial. Moreover, we also propose an improved RFID authentication protocol that employs Chebyshev chaotic maps and complies with the EPCglobal Class 1 Generation 2 standard. Finally, we show that our protocol is resistant against those security issues.