In this paper, we propose a Timed Efficient and Secure Vehicular Communication (TSVC) scheme with privacy preservation, which aims at minimizing the packet overhead in terms of signature overhead and signature verification latency without compromising the security and privacy requirements. Compared with currently existing public key based packet authentication schemes for security and privacy, the communication and computation overhead of TSVC can be significantly reduced due to the short message authentication code (MAC) tag attached in each packet for the packet authentication, by which only a fast hash operation is required to verify each packet. Simulation results demonstrate that TSVC maintains acceptable packet latency with much less packet overhead, while significantly reducing the packet loss ratio compared with that of the existing public key infrastructure (PKI) based schemes, especially when the road traffic is heavy.Index Terms-Vehicular communications, security, TESLA, hash chain.