Geographic Opportunistic Routing (GOR) tries to avariciously send a message from source node to the closest neighboring node that's the highest priority toward the packet's destination at road Intersection in VANETs. Geographic Opportunistic Routing (GOR) may well be an advanced and efficient routing technique that was associated decent, economical and heightens routing scheme for VANETs. Vehicular Ad-Hoc Networks (VANETs) is a special type of wireless networks. In VANETs, the foremost challenge is that the extraordinarily dynamic property of mobile nodes (i.e., high mobility), therefore the extraordinarily dynamic topology suggests that topology changes over times. In this paper, we have a tendency to propose a new distributed geographical opportunistic routing protocol for vehicular ad-hoc situations referred to as Distributed Geographical Opportunistic Routing (DGOR) protocol. To handle the node mobility, direction, and speed, we've got propose a new replacement metric that considers the geographical location of the vehicles, the amount of the neighboring nodes at road Intersection, and therefore the expected position of nodes victimization the motion vector of the vehicular nodes at road Intersection. We have introduced DGOR problem in Vehicular Ad-Hoc Networks at road Intersection and this problem is NP-complete. A O(nlogn) approximation algorithm is designed to solve the DGOR problem for Vehicular Ad-Hoc Networks at road Intersection. © 2017 IEEE.