Recently, many researches on Vehicular Ad Hoc Networks (VANETs) have been performed because of the many related applications. Data dissemination is among the challenging issues face by these kinds of networks to overcome several problems, such as broadcast storm, and network fragmentation. In this respect, the present work proposes a new Geocast-based Safety Information Dissemination protocol for VANETs, called Geo-SID. The proposed protocol is used for dissemination of safety information in a V2V scenario. It is specifically designed and suitable for an urban environment. The main goal of Geo-SID scheme is to perform the safety information dissemination process within a Zone of Relevance (ZoR) and without using the Zone of Forwarding (ZoF) similar to existing dissemination protocols in the literature. Furthermore, our solution aims to eliminate the broadcast storm problem by avoiding irrelevant alert messages and providing an efficient safety data dissemination across a ZoR area by extending the coverage area, reducing the network overhead and improving the latency. We simulate our proposed protocol using network simulator NS-3 and SUMO environment. Our proposed protocol outperforms similar protocols available in the literature based on the obtained simulation results.