The safety applications for cooperative driving in VANETs, typically require the dissemination of safety-related information to all vehicles with high reliability and a strict timeline. However, due to the high vehicle mobility, dynamic traffic density, and a self-organized network, Safety message dissemination has a special challenge to efficiently use the limited network resources to satisfy its requirements. With this motivation, we propose a novel broadcasting protocol referred to as congestion awareness multi-hop broadcasting (CAMB) based loosely on a TDMA-like transmission scheduling scheme. The proposed protocol was evaluated using different traffic scenarios within both a realistic channel model and an 802.11p PHY/MAC model in our simulation. The simulation results showed that the performance of our CAMB protocol was better than those of the existing broadcasting protocols in terms of channel access delay, packet delivery ratio, end-to-end delay, and network overhead.