Radio frequency identification (RFID) system has gained attention as a new identification source that achieves a ubiquitous environment. Each RFID tag has a unique ID and is attached to an object. A user reads the unique ID of an RFID tag by using RFID readers and obtains the information on the object. One of the important technologies that use the RFID systems is the position estimation of RFID tags. Position estimation means estimating the location of the object with the RFID tag. Acquiring the location information of the RFID tag can be very useful. If a user can know the position of the RFID tag, the position estimation can be applied to a navigation system for walkers. In this paper, we propose a new position estimation method named Swift Communication Range Recognition (S-CRR) as an extended improvement on previous CRR that shortens the estimation delay. In this method, the position of an RFID tag is estimated by selecting the communication area model that corresponds to its boundary angles. We evaluated its performance by experiments and simulations of the RFID system. As the results, we found that S-CRR can estimate the position of an RFID tag comparatively accurately and quickly.