In vehicular ad hoc networks (VANETs), mobility between vehicles can cause rapid topology changes with frequent disconnections, which result in collisions and packet losses that make communications unstable. Alternatively, cooperative transmission can increase the reliability of communication by eliminating these problems in VANETS. In heavy traffic conditions, carrier sense multiple access with collision avoidance (CSMA/CA) suffers from collision, and it is not effective when high data rate is required. Therefore, orthogonal frequency division multiple access (OFDMA) is proposed. With the use of OFDMA, throughput is increased and delay is decreased by reducing the probability of collision in high traffic scenario. In this study, a novel OFDMA based efficient cooperative MAC protocol (OEC-MAC) is proposed for VANETs. Subcarrier channels assignment and access mechanisms are provided. The mechanism is presented not only for choosing the appropriate transmission mode but also for selecting the optimum relay. New control messages are defined to support cooperative communication. The performance of OEC-MAC protocol is examined by providing analytical analysis based on Markov chain model. Numerical results are demonstrated, which reveal that OEC-MAC protocol ensures a remarkable increase in throughput and also satisfies the strict delay requirement of 100 ms in VANETs for safety messages (sm). In addition, communication reliability is increased by reducing the packet dropping rate (PDR). Numerical results are compared with existing protocols, and a quantitative comparison is provided. It has been seen form results that proposed OEC-MAC protocol is better than existing schemes, especially under heavy traffic scenarios.