The maritime wideband communication network, which extends the operation of wireless access from land to sea, will significantly contribute to the maritime distress, urgency, safety, and general communications. The Worldwide Interoperability for Microwave Access (WiMAX) technology has been applied to establish a maritime wideband shore-side network infrastructure, to achieve large capacity data backhauls. However, in this scenario, many new security and privacy challenges are arising, e.g., the reduced time overhead for group access authentication due to limited time window vessels passing by infostations along the shore-side. In this paper, a simple and reliable group authentication framework is developed for dealing with security issues in this special maritime wideband communication scenario. Specifically, an efficient authentication protocol for secure group communications (EAPSG) in maritime wideband communication network is proposed based on the Elliptic Curve Diffie-Hellman (ECDH), to overcome the weakness existing in the prevailing protocols on land, i.e., user identity disclosure, the lack of perfect forward secrecy, and man-in-the-middle attacks. Meanwhile, EAPSG can reduce the communication overhead and computational complexity by designing group access authentication procedures. Compared with conventional EAP-AKA protocol used in WiMAX networks on land, our scheme enhances the security and provides better performance. Especially, the security of the proposed protocol was verified by Automated Validation of Internet Security Protocols and Applications (AVISPA), and detailed performance evaluations are also given. The results illustrate that the proposed EAPSG outperforms other existing schemes on land in terms of the delivery cost and the number of signaling messages.