Recent years have witnessed that the new mobility Intelligent Transportation System is booming, especially the development of Vehicular Ad Hoc Networks (VANETs). It brings convenience and a good experience for drivers. Unfortunately, VANETs are suffering from potential security and privacy issues due to the inherent openness of VANETs. In the past few years, to address security and privacy-preserving problems, many identity-based privacy-preserving authentication schemes have been proposed by researchers. However, we found that these schemes fail to meet the requirements of user privacy protection and are vulnerable to attacks or have high computational complexity. Hence, we focus on enhancing privacy-preserving via authentication and achieving better performance. In this paper, first, we describe the vulnerabilities of the previous scheme. Furthermore, to enhance privacy protection and achieve better performance, we propose an efficient privacy-preserving mutual authentication protocol for secure V2V communication in VANETs. Through security analysis and comparison, we formally demonstrate that our scheme can accomplish security goals under dynamic topographical scenario compared with the previous scheme. Finally, the efficiency of the scheme is showed by performance evaluation. The results of our proposed scheme are computationally efficient compared with the previously proposed privacy-preserving authentication scheme.