As physical obstacles, vehicles have significant impacts on the efficient propagations of safety-related information in vehicular ad hoc networks (VANETs) by frequently obstructing the LOS links between transmitters and receivers. Obstructing effect will diminish the effective coverage of safety-related information and incur severe impact on road safety. However, this impact has not been addressed effectively. In this paper, we first present the definition of broadcast efficiency as the metric for quantizing the obstructing effect. We investigate the optimization issue for mitigating the impact of obstructing effect on the propagation of safety-related information and propose a graph theory-based optimization algorithm. For a distributed implementation of this optimization in VANETs, we further propose the maximum broadcast efficiency relaying (MBER) algorithm. MBER maximizes the effective coverage of information, meanwhile, meets delay and reliability constraints by incorporating broadcast efficiency and propagation distance in relay contention. Simulation results demonstrate that MBER promotes the effective coverage of safety-related information in VANETs with varying vehicular distribution.