Vanets are new emerging and challenging technology that makes an improvisation in traffic safety and efficiency. The constant growth of automobile industry is increasing the demand for car safety and the car to car connectivity. It creates a path for intelligent transportation system(ITS).The information that is carried by the vehicles can enrol safety measures The group-oriented services are one of the primary application classes that are addressed by VANETs in recent years. To support such services, multicast routing is used. Thus, there is a need to design stable and reliable multicast routing protocols for VANETs to ensure better packet delivery ratio, lower delays and reduced control overheads. In this paper, we propose link stability based hop by hop multicast routing scheme that finds stable multicast path from source to receivers. The multicast path is constructed by using route request and route reply packets with the help of multicast routing information cache and link stability database maintained at every node. A multicast routing protocol that implements multicast distribution through recursive unicast trees. The main goals of LSHBH are to support unicast clouds, allowing incremental deployment to have a stable tree structure, by minimizing the impact of receiver departures, and to construct low-cost trees, to reduce administrative costs and to lower error rate. The proposed scheme is simulated over a large number of VANET nodes with wide range of mobility and the performance is evaluated. It is observed that proposed scheme produces better packet delivery ratio, less control overheads and reduced packet delay compared to on-demand multicast routing protocol (ODMRP).