Vehicular Ad-Hoc Networks (VANETs) play a crucial role in improving traffic efficiency and road safety through the exchange of critical information among vehicles. Recently, many researchers have proposed various privacy-preserving authentication protocols for secure communication in VANETs. However, most of the protocols suffer from un-linkability, higher computation, and communication overheads. To solve the aforementioned issues in VANETs, we present a lightweight mutual authentication and privacy-preserving protocol that significantly reduces computation and communication overheads of Trusted Authority (TA) and vehicles. Security verification demonstrates that our proposed protocol is secure against various prevalent cryptographic attacks. Moreover, the performance analysis illustrates the efficiency of our proposed work in comparison with existing works. Effectiveness of our proposed work makes it suitable for secure message transmission among vehicles in VANETs.