The development of Internet of things has spawned the vehicular ad hoc network (VANET), which facilitates the safe and comfortable driving. The communications in VANET should be protected to deter against message leakage and modifications. To solve the security issues in VANET communications, we present a dynamic and efficient authenticated group key agreement (AGKA) protocol SC-AGKA with conditional privacy employing the self-certified cryptosystem, and prove its security based on the computational Diffie-Hellman problem. Our SC-AGKA protocol establishes a group key among multiple group users and achieves conditional privacy for the group users. Based on our SC-AGKA protocol, we propose an authentication and group key agreement protocol applying the design in VANET. Additionally, we also notify that through performance comparisons, our protocol has higher security and efficiency in computation and communication compared to other AGKA designs.