A Wi-Fi fingerprint consists of received signal strength values at a particular location along with the location information. A Wi-Fi radio map is constructed by maintaining a database of Wi-Fi fingerprints at various points in a building. A city radio map is a collection of radio maps for most buildings in a city. A highly precise citywide indoor positioning service is possible, if an accurate city radio map is available. However, tremendous time and effort are required to construct a city radio map through manual calibration. This paper proposes a method for constructing a city radio map through the crowdsourcing of Wi-Fi fingerprints from numerous smartphones. The proposed method classifies the buildings in a city into three categories: buildings in residential areas, commercial areas, and public areas. Then, it develops location-labeling techniques appropriate for the collected fingerprints from buildings in each category. Experiments conducted in the cities of Daejeon and Seoul revealed that the proposed method can construct a precise city radio map with minimal cost in a short period of time. Once city radio maps are constructed for most cities around the world, the global indoor positioning system will be completed.