Users tend to check in and post their statuses in location- based social networks (LBSNs) to describe that their in- Terests are related to a point-of-interest (POI). Since the relevance of the data to the POI varies according to the ge- ographic distance between the POI and the locations where the data are generated, it is important to characterize an area-of-interest (AOI) that enables to utilize the location information in a variety of businesses, services, and place advertisements. While previous studies on discovering AOIs were conducted based mostly on density-based clustering methods with the collection of geo-tagged photos from LB- SNs, we focus on detecting a POI boundary, which corresponds to only one cluster containing its POI center. Using geo-tagged tweets recorded from Twitter users, this paper introduces a low-complexity two-phase strategy to detect a POI boundary by finding a suitable radius reachable from the POI center. We detect a polygon-type boundary of the POI as the convex hull (i.e., the outermost region) of selected geo-tags through our two-phase approach, where each phase proceeds on with different sizes of radius increment, thus yielding a more precise boundary. It is shown that our approach outperforms the conventional density-based clustering method in terms of runtime complexity.