Abstract: Secure Wireless Roaming (SWR) allows a roaming user under the subscription of its home server to establish a secure session key with a foreign server in an authenticated way such that both the foreign server and the roaming user can mutually authenticate each other. Anonymous SWR provides an additional service to the roaming user so that the roaming user can keep anonymous and untraceable even if all the visited foreign servers are colluding with each other. In this paper, an anonymous SWR called SYM-SWR (SYMmetric key based SWR) is proposed. To best of our knowledge, it seems to be the first pure symmetric key based anonymous SWR. Compared with other existing SWR protocols both of the computation complexity and communication complexity of SYM-SWR are lowest, since it involves only 4 message flows and no PKI (Public Key Infrastructure) but only highly efficient cryptographic operations are needed which include Message Authentication Code (MAC) and symmetric key encryption.