Recently, the platoon-based vehicular cyber-physical system VCPS has attracted significant attention because the platoon based driving pattern can bring many benefits. In the platoon-based VCPS, the platoon members may change quite dynamically because vehicles can join or leave the platoon at any time. Therefore, how to securely and efficiently set up and maintain a platoon is a challenge. To address this issue, in this paper, we propose a secure and privacy-preserving group setup framework, called SPGS, for platoon-based VCPS. The key components of SPGS are two group setup policies that can be developed based on two kinds of techniques: attribute-based encryption and contributory key agreement. Based on these group setup policies, we propose two authentication protocols, respectively. The first one can authenticate all vehicles in the platoon simultaneously. The second one can guarantee anonymous authentication with traceability. With SPGS, a temporary platoon can be securely set up and maintained, and platoon merging/splitting can also be flexibly supported. Finally, we carry out extensive analysis to show the security and efficiency of our proposed SPGS. Copyright © 2016 John Wiley & Sons, Ltd.