The convergence of third generation (3G) wide area wireless network and wireless local area network (WLAN) offers characteristics that complement each other perfectly. To provide secure 3G-WLAN convergence, extensible authentication protocol-authentication and key agreement (EAP-AKA) protocol, that has got many risk, is used. This paper elaborate risks in using EAP-AKA for 3G-WLAN convergence, proposes an authentication and key agreement protocol that combines elliptic curve Diffie-Hellman (ECDH) with symmetric key cryptosystem. The proposed protocol when analysed using simulation tool shows that it not only overcomes the risk, it ensures optimal quality of service (QoS) because of its less delay for authentication compared to EAP-AKA.