In GSM-WLAN heterogeneous networks, the authentication efficiency is one of the drawbacks for message transaction and processing in the RADIUS server. This paper proposed two fast authentication schemes, based on the EAP-SIM mechanism, to improve the authentication efficiency by balancing the message transaction loads and processing loads among the RADIUS server and individual APs. In this paper, the IEEE 802.11 WLAN simulation mode based on the Network Simulator 2 (NS-2) is used to evaluate the performance including the authentication session time, message transaction load and processing load for the proposed authentication schemes and the conventional EAP-SIM authentication schemes. The results show that the proposed full authentication scheme can save about 20% authentication session time compared to the conventional full authentication scheme, and the proposed iterative fast authentication scheme can save about 75% authentication session time compared to the conventional fast re-authentication scheme. Therefore, the authentication efficiency of the proposed schemes is better than that with the conventional authentication schemes.