Secure communications for vehicular ad hoc networks (VANETs) have become an important research issue these years. Many protocols for secure vehicle-to-vehicle communications and vehicle-to-infrastructure communications have been proposed, yet fewer protocols are concerned with secure group communications for VANETs. Of those existing protocols for group communications, some of them form a group of vehicles based on geographical regions and provide broadcasting to the group members with or without message confidentiality. The others allow secure vehicle-to-vehicle communications within a group with session keys, but they do not preserve user privacy for communicating parties within the group. In this paper, we propose a novel group communication scheme for vehicular networks, in which a group is formed by a set of related vehicles of the same purpose, such as a platoon of recreational vehicles targeted for the same tourist spot. The scheme not only offers efficient and secure group communications but also provides privacy preservation for vehicle-to-vehicle communications within a group. Security analysis is given to demonstrate the robustness of the proposed scheme.