Designing MAC protocol for vehicle ad hoc networks (VANETs) is challenging because of quick topology changes, high vehicle mobility, and different quality of service requirements. One promising approach is to employ both TDMA and CSMA hybrid access schemes in the control channel interval. These protocols can adjust the length of TDMA frame (also called broadcast frame) to adapt itself to different vehicle conditions and provide efficient non-safety message transmission. To improve the efficiency of the hybrid MAC mechanism in VANET, we propose an efficient and fast broadcast frame adjustment algorithm, called EFAB based on the three-hop neighbor information. By adjusting the broadcast frame length quickly, MAC protocol using EFAB can support efficient broadcast services on the control channel. Simulation results show that the hybrid MAC protocol using EFAB can provide faster broadcast frame adjustment and higher packet delivery ratio of safety packets on the control channel than using the existing algorithms.