The VeMAC, a TDMA-based MAC protocol for Vehicular Ad-hoc NETworks (VANET), assigns disjoint sets of the time slots to vehicles moving in opposite directions and to road side units. So the VeMAC protocol reduces the access and merging collisions. Moreover, the VeMAC protocol employs slot release prevention condition which avoids unnecessarily releasing time slots when a node just enters the communication range of each other. Although VeMAC supports reliable and efficient transmission, it is still not full applicable for VANET in parallel transmission. In this paper, we propose an e-VeMAC protocol: an enhanced vehicular MAC protocol to mitigate the exposed terminal problem. The simulation results show that the e-VeMAC protocol supports more parallel transmissions than the VeMAC protocol.