The Internet of Vehicles (IoV) provides an important platform for various applications in diverse vehicular sectors such as the safety, energy-saving, decision-making, routing, and entertainment, which makes vehicular transportation safer, greener, and easier. While providing convenient and efficient communications between vehicles, the wireless channel in IoV also faces an eavesdropping problem in the security area due to its open and shared nature. Different from the previous works under asymmetric assumptions, this paper studies a covert communication problem within symmetrical assumption, to prevent the eavesdropper from sensing the vehicular communications when the vehicles and eavesdropper have the same ability. Firstly, by dividing the network area into the safe area, dangerous area, and gray area, we show that with the help of a friendly jamming, all vehicular communications in the safe area can be covert. Secondly, by presenting a distributed jammer election algorithm with asymptotically optimal running time, we give an approach to obtain a friendly jammer from the vehicles for the covert communications. Finally, a comprehensive framework is presented, to convert the vehicular algorithms without covert communications into the ones only consisting of covert communications with their time complexity constant times increased as the trade-off. Empirical results validate the time efficiency of our covert communication algorithms with jammer election on running time.(C) 2022 Elsevier Inc. All rights reserved.