WIFI-based received signal strength indicator (RSSI) fingerprinting is widely used for indoor localization due to desirable features such as universal availability, privacy protection, and low deployment cost. The key of RSSI fingerprinting is to construct a trustworthy RSSI map, which contains the measurements of received access point (AP) signal strengths at different calibration points. Location can be estimated by matching live RSSIs with the RSSI map. However, a fine-grained map requires much labor and time. This calls for developing efficient interpolation and approximation methods. Besides, due to environmental changes, the RSSI map requires periodical updates to guarantee localization accuracy. In this paper, we propose a spatio-temporal (S-T) similarity model which uses the S-T correlation to construct a fine-grained and up-to-date RSSI map. Five S-T correlation metrics are proposed, i.e., the spatial distance, signal similarity, similarity likelihood, RSSI vector distance, and the S-T reliability. This model is evaluated based on experiments in our indoor WIFI positioning system test bed. Results show improvements in both the interpolation accuracy (up to 7%) and localization accuracy (up to 32%), compared to four commonly used RSSI map construction methods, namely, linear interpolation, cubic interpolation, nearest neighbor interpolation, and compressive sensing.