New cellular networks are capable of providing high mobility, whereas WLANs are known for having relatively higher bandwidths. Therefore, interworking cellular networks with WLANs offers ubiquitous data services and relatively high data rates across modern networks. This interworking will enable a user to access new cellular services via a WLAN, while roaming within a range of hotspots. To provide secure 3G-WLAN interworking in the SAE/LTE architecture, Extensible Authentication Protocol-Authentication and Key Agreement (EAP-AKA) is used. However, EAP-AKA has several vulnerabilities. This paper analyzes vulnerabilities in LTE-WLAN interworking and proposes a new authentication and key agreement protocol based on EAP-AKA.