Empirical models of Total Electron Content (TEC) based on functional fitting over Taiwan (120° E, 24° N) have been constructed using data of the Global Positioning System (GPS) from 1998 to 2007 during geomagnetically quiet condition (D_st>−30 nT). The models provide TEC as functions of local time (LT), day of year (DOY) and the solar activity (F), which are represented by 1–162 days mean of F10.7 and EUV. Other models based on median values have been also constructed and compared with the models based on the functional fitting. Under same values of F parameter, the models based on the functional fitting show better accuracy than those based on the median values in all cases. The functional fitting model using daily EUV is the most accurate with 9.2 TECu of root mean square error (RMS) than the 15-days running median with 10.4 TECu RMS and the model of International Reference Ionosphere 2007 (IRI2007) with 14.7 TECu RMS. IRI2007 overestimates TEC when the solar activity is low, and underestimates TEC when the solar activity is high. Though average of 81 days centered running mean of F10.7 and daily F10.7 is often used as indicator of EUV, our result suggests that average of F10.7 mean from 1 to 54 day prior and current day is better than the average of 81 days centered running mean for reproduction of TEC. This paper is for the first time comparing the median based model with the functional fitting model. Results indicate the functional fitting model yielding a better performance than the median based one. Meanwhile we find that the EUV radiation is essential to derive an optimal TEC.