Cognitive radio (CR) technology has been offered to improve efficiency in bandwidth use and the quality of service (QoS) of heterogeneous wireless networks with varied types of radio systems. As the CR network system grows, network security has been raised as an area of concern. The topic has yet to be fully considered and no suitable authentication methods have been identified. In this paper, we propose a radio-free mutual authentication protocol for the CR network. The protocol, named EAP-CRP, adopts the location information of a mobile terminal as a shared secret for authentication. EAP-CRP has been designed to satisfy the requirements of wireless network security, confidentiality, integrity and availability, and is realized as a lightweight and quick-responding mutual authentication protocol.