As physical obstacles, vehicles have a significant impact on the efficient propagation of safety-related information in vehicular ad hoc networks (VANETs) by frequently obstructing the LOS link between the source and receivers. Obstructing effect of vehicles will diminish the effective coverage of broadcast as part of vehicles can not decode the broadcast successfully and incur severe impact on road safety. However, this impact has not been addressed by existing protocols. In this paper, we first present the definition of broadcast efficiency (BE) as the metric for measuring the obstructing effect and conclude the optimization issue of propagation. We further propose a distributed algorithm for mitigating this impact that can be embedded in VANETs. This algorithm maximizes the effective coverage of the broadcast of safety-related information and meanwhile satisfies the constraints on both link state and delay by selecting relay according to BE and referential propagation distance. Simulation results demonstrate that the proposed algorithm promotes the efficiency of propagation in dynamic multilane VANETs with varying vehicular distribution.