Location privacy is an interesting problem that has been receiving considerable attention. This problem has been widely discussed from the individual point of view; however, there exist only a few works that support location privacy for a group of users. In this paper we consider the problem of supporting location privacy for a group of users during the use of location-based services (LBSs). We assume a group of users who want to benefit from a LBS and find the nearest meeting place that minimizes their aggregate distance. Each user in this scenario wants to protect his or her location from the LBS, outside attackers, and other group members. We show that individual solutions for location privacy cannot be directly applied to the group location privacy problem and a special solution must be developed. We identify the privacy issues for this group scenario and propose a resource-aware solution in order to satisfy these group privacy issues. Our solution is based on secure multiparty computation and the anonymous veto network protocol. The proposed protocol decreases the number of group queries to a large extent, as it only sends a single query to the LBS. Consequently, the LBS overhead to evaluate the query and the size of the LBS result are significantly decreased. The proposed protocol also protects the LBS from the excessive disclosure of points of interest and the LBS provider only needs to apply an existing private nearest neighbor (NN) query algorithm instead of an aggregate NN query algorithm. The performance and security analysis show that the protocol is secure against a partial collusion attack and a denialof-service attack in a malicious model.