Vehicle-based applications were recently introduced to improve traffic safety and efficiency. These applications are classified into either safety-oriented or non-safety-oriented applications. Safety-oriented applications are typically provided by means of vehicle-to-vehicle (V2V) communications to support reliable and fast alert message propagation to all surrounding vehicles when an emergency occurs on the road. In vehicular ad-hoc network (VANET) broadcast-based packet forwarding is typically preferred for the propagation of urgent traffic-related information to all reachable nodes within a specified dangerous region. However, this approach may cause broadcast storm problems, which can lead to serious contention between transmissions from adjacent nodes. In this paper, we propose an alert message propagation scheme that is based on selective forwarding and aims to i) minimize the number of rebroadcasting nodes and ii) guarantee reliable and fast alert message delivery to all reachable nodes. Our scheme was evaluated using two different highway scenarios. The simulation results demonstrated that the performance of the proposed scheme was better than that of existing broadcast schemes in terms of the message delivery latency, the message delivery ratio, and the message rebroadcasting ratio.