With the widespread development of the Internet, the Internet of Things (IoT) technology has been popularly applied to many applications, for example, network appliances, automation and control, and people position. In recent years with the aging population trend, not only the health care of elderly people but also problems associated with the loss of wisdom of the elderly has attracted increasing attention. Moreover, how to monitor elderly people has also become a very popular topic. The radio-frequency identification (RFID) technology has been developed for localization applications. However, LANDMARC, a location-sensing prototype system that uses RFID technology for locating objects inside buildings, is too expensive owing to the highly dense deployment of tags. Therefore, in this paper, a low-cost system based on RFID technology is proposed for elderly people. Furthermore, to increase the efficiency and quality of care, fuzzy logic is added to the proposed monitoring system. On the other hand, we use a time-sensitive alert marquee, email, and push notification function to give an alarm for elderly people who stay too long in the bathroom or other locations outside. The results show that caregivers can clearly monitor the positions of elderly people through the RFID-based localization system with fuzzy logic.