Currently, vehicular ad-hoc network (VANET) is one of the most successful mobile ad-hoc network (MANET) commercially. Vehicles use two kind of messages named Safety Alert Message in order to advertise their change of status. One of them is periodic safety message (PSM), the other is event driven safety message (EDS) which occurs as soon as the vehicles' status change abnormally. (i.e. change in speed or direction). As the control channel has to share the sync interval (SI) with the service channels, access to the control channel by the safety message is delayed during the service channel interval (SCHI). All safety messages generated during SCHI attempt to access as soon as control channel interval (CCHI) starts, which could result in flash crowd problem for the safety applications. In this paper, we propose group-based distributed periodic access scheme for the safety messages. This scheme uses hashing function to distribute the access time of the safety message into CCHI instead of SI within one group which is led by group leader (GL) using advanced grouping method.