Due to vehicle movement and lossy wireless channels, providing a reliable and efficient multi-hop broadcast service in vehicular ad hoc networks (VANETs) is a well-known challenging problem. In this paper, we propose BR-NB (broadcast with neighbor information), a fuzzy logic based multi-hop broadcast protocol for VANETs. BR-NB achieves a low overhead by using only a subset of neighbor nodes to relay data packets. For the relay node selection, BR-NB jointly considers multiple metrics of the inter-vehicle distance, vehicle mobility and link quality by employing fuzzy logic. Since the expected coverage and vehicle mobility are inferred from the two-hop neighbor information which can be acquired from the hello message exchange, BR-NB is independent of position information. BR-NB provides a practical and portable solution for broadcast services in VANETs. We use computer simulations and real-world experiments to evaluate the performance of BR-NB.