In this study, an empirical model constructed using data of FORMOSAT3/COSMIC (F3/C) from 29 June, 2006, to 17 October, 2009, retrieves altitude profiles of electron density (Ne). The model derives global Ne profiles from 150 to 590 km altitude as functions of the solar EUV flux, day of year, local time and location under geomagnetically quiet conditions (Kp < 4). Ne profiles derived by the model are further compared with those of the International Reference Ionosphere (IRI). Results show that the F2 peak altitude hmF2 and the electron density NmF2, as well as the electron density above, derived by the model are lower than those of the IRI model. The F3/C model reproduces observations of F3/C well at 410-km altitude while the IRI model overestimates them. The overestimation of the IRI model becomes large with decrease of EUV flux. It is found that the topside vertical scale height of the F3/C model shows high values not only magnetic dip equator but also middle latitude. The results differ significantly from those of IRI, but agree with those observed by topside sounders, Alouette and ISIS satellites.