Vehicular ad hoc networks have been attracting the interest of both academic and industrial communities on account of their potential role in Intelligent Transportation Systems (ITS). In vehicular ad hoc networks, vehicles are usually located quite densely within the range of radio transmission. In this paper, we propose a fuzzy logic based multi-hop broadcast protocol for information dissemination in high-density vehicular ad hoc networks. The proposed protocol exhibits low message overheads by means of using only a subset of neighbor nodes to relay messages. In the relay node selection, the proposed protocol jointly considers multiple metrics of inter-vehicle distance, node mobility and signal strength by employing the fuzzy logic. We use computer simulations to evaluate the performance of the proposed protocol.