A radio map is a collection of fingerprints and collected location information. To build more accurate Wi-Fi positioning system (WPS), a more precise radio map should be prepared in advance. Despite GPS signals are usually unreachable in most indoor venues, GPS signals are commonly used as reference locations to tag the collected fingerprints. As a result, WPS has not been able to achieve high performance in accuracy indoors, even if the place is rich in Wi-Fi signals. This paper introduces a novel method to construct a radio map without any use of GPS signals. Users' home or office address is used instead to tag the locations of collected Wi-Fi signals. Since the method utilizes Wi-Fi signals collected indoors, a more precise radio map construction is possible. For evaluation, we tested the method at four deliberately selected residential and downtown areas in Daejeon and Seoul, Korea. Once the data collection rate rises above 50%, the average error distance was within 10m or less. This indicates that address-based crowdsourcing radio map construction can be an effective means to construct global-scale but precise radio maps at low cost.