The third generation partnership project (3GPP) has addressed the feasibility of interworking andspecified the interworking architecture and security architecture for third generation (3G)-wireless localarea network (WLAN), it is developing, system architecture evolution (SAE)/ long term evolution (LTE)architecture, for the next generation mobile communication system. To provide a secure 3G-WLANinterworking in the SAE/LTE architecture, Extensible authentication protocol-authentication and keyagreement (EAP-AKA) is used. However, EAP-AKA have several vulnerabilities. Therefore, this papernot only analyses the threats and attacks in 3G-WLAN interworking but also proposes a newauthentication and key agreement protocol based on EAP-AKA. The proposed protocol combines ellipticcurve Diffie-Hellman (ECDH) with symmetric key cryptosystem to overcome the vulnerabilities. Theproposed protocol is used in hybrid coupled 3G-WLAN convergence network to analyse its efficiency interms of QoS metrics, the results obtained using OPNET 14.5 shows that the proposed protocoloutperforms existing interworking protocols both in security and QoS.