The recent development of vehicular networking technologies brings the promise of improved driving safety and traffic efficiency. Cooperative communication is recognized as a low-complexity solution for enhancing both the reliability and the throughput of vehicular networks. However, due to the openness of wireless medium, the vehicular wireless communications (VWC) is also vulnerable to potential eavesdropping attacks. To tackle with this issue, we in this paper propose a novel user-cooperation scheme with anti-eavesdropping capabilities. Specifically, prior to any frame transmission, a source-relay pair is jointly selected to maximize the achievable secrecy rate. After that, the selected relay assists the source to deliver its data to the destination. The proposed selection scheme can be realized in a fully distributed manner, and the security is guaranteed without using any encryption techniques at the upper layers. The closed-form expressions for the secrecy outage probability and the intercept probability are derived, and the achievable diversity order is also analyzed. Simulation results show that the proposed scheme outperforms the competing counterparts in terms of both the secrecy outage probability and the average secrecy rate.