Demand for care services, especially for children and the elderly, has been increasing. Several GPS-based pedestrian tracking systems have been researched and developed, but GPS cannot provide accurate position estimates in high-rise areas and indoor environments. In order to settle this issue, we propose a pedestrian tracking system that uses Wi-Fi beacons held by target persons and Wi-Fi access points placed widely and densely in a specified area. Target users’ positions are estimated on the basis of probe request signals broadcast by the Wi-Fi beacons. The positioning algorithm is based on proximity detection based on received signal strength. In addition, the proposed method uses a computation time reduction strategy and error reduction techniques. Each target’s trajectory is estimated on the basis of position estimates using several trajectory correction algorithms. Experimental results show that the proposed positioning system can estimate a target’s trajectory with approximately 80% accuracy, with a positioning delay, i.e., time taken to estimate a target’s position, of approximately 2.8s.