Vehicle Ad-hoc Networks (VANETs) have experienced significant development in recent years, playing a crucial role in enhancing the driving experience by enabling safer and more efficient inter-vehicle interactions through information exchange. Vehicle-to-vehicle (V2V) communication is particularly vital as it not only helps to prevent collisions and improve traffic efficiency but also provides essential situational awareness to drivers or autonomous driving systems. Communication is typically supported by Roadside Units (RSUs); however, in practical applications, vehicles may exceed the communication range of RSUs, thus exposing them to various malicious attacks. Additionally, considering the limited computational resources of onboard units (OBUs) in vehicles, there is a high demand for designing lightweight security protocols that support V2V communication. To address this issue, this paper proposes an efficient anonymous V2V identity authentication protocol tailored for scenarios that lack RSU support. The proposed protocol has been formally assessed using the Scyther tool, demonstrating its capability to withstand major typical malicious attacks. Performance evaluations indicate that the proposed protocol is efficient in terms of communication and computational overhead, making it a viable solution for V2V vehicle communication.