Although accurate positioning systems are important to provide location-aware services, solutions that are applicable in high-rise areas and inside buildings have not yet been realized. We propose an accurate positioning system that utilizes widely and densely placed Wi-Fi access points. The proposed system utilizes probe request signals broadcast by mobile devices to estimate their positions. The positioning algorithm is based on proximity detection using received signal strength indication. In addition, the proposed method employs a computation time reduction strategy and error reduction techniques. The proposed system can also show pedestrian flow, which is valuable information for developing shop branching plans, street improvement, and so on. The experimental results show that the proposed positioning system achieved an accuracy of 5.36 m. The system can also visualize pedestrian flow trends in a given Wi-Fi coverage area based on the position estimates.