© 2017 by the authors. Licensee MDPI, Basel, Switzerland. Mobile sink groups play crucial roles to perform their own missions in many wireless sensor network (WSN) applications. In order to support mobility of such sink groups, it is important to design a mechanism for effective discovery of the group in motion. However, earlier studies obtain group region information by periodic query. For that reason, the mechanism leads to significant signaling overhead due to frequent flooding for the query regardless of the group movement. Furthermore, the mechanism worsens the problem by the flooding in the whole expected area. To deal with this problem, we propose a novel mobile sink group support scheme with low communication cost, called Region-Shift-based Mobile Geocasting Protocol (RSMGP). In this study, we utilize the group mobility feature for which members of a group have joint motion patterns. Thus, we could trace group movement by shifting the region as much as partial members move out of the previous region. Furthermore, the region acquisition is only performed at the moment by just deviated members without collaboration of all members. Experimental results validate the improved signaling overhead of our study compared to the previous studies.